Braise veal: Position oven racks in upper and lower thirds of oven and preheat to 325°F.
Pat veal dry and sprinkle with salt and pepper. Heat oil and 1 tablespoon butter in 5- to 6-quart pot over moderately high heat until foam subsides, then brown veal on all sides, turning with tongs, about 10 minutes. Transfer veal to a plate and discard fat from pot.
Melt remaining tablespoon butter in pot and cook onion, celery, and carrot over moderate heat, stirring and scraping up any brown bits, until softened, about 5 minutes.
Wrap parsley, fresh thyme (if using), and bay leaf in a square of cheesecloth and tie into a bundle with string to make a bouquet garni, then add to vegetables along with wine and dried thyme (if using). Put veal on top and bring to a simmer.
Cover pot with lid, then transfer to lower third of oven and braise veal until thermometer inserted 2 inches into center of meat registers 145°F, about 1 1/2 hours.
Transfer veal to a cutting board and let stand 30 minutes (internal temperature will rise to 155°F). Pour cooking juices from pot through a fine-mesh sieve into a 4-cup measure, pressing on and discarding solids. Skim off fat and reserve juices, adding any juices that have accumulated on plate from veal, for Mornay sauce.
Make soubise while veal braises: Parcook rice in a large saucepan of boiling salted water 5 minutes, then drain in a sieve and rinse.
Heat butter in a 10-inch ovenproof skillet over moderately low heat until foam subsides, then stir in onions and salt. Cover tightly with a lid or a double layer of foil and cook onions over low heat, stirring occasionally, 5 minutes. Stir in rice and broth and bring to a simmer.
Cover skillet tightly, then transfer to upper third of oven and bake until rice and onions are very soft, about 1 hour. (Leave oven on.)
Transfer soubise to a food processor and pulse until coarsely puréed. Transfer to a bowl to cool.
Make duxelles while veal and soubise cook: Put a handful of mushrooms in a clean kitchen towel (not terry cloth), then gather towel around mushrooms and wring them over sink to squeeze out as much liquid as possible. Wring out remaining mushrooms, a handful at a time, in same manner.
Heat butter in a 12-inch heavy skillet over moderately high heat until foam subsides, then sauté mushrooms and truffles (if using), stirring, until lightly browned and any liquid mushrooms give off is evaporated, 6 to 8 minutes. Stir in cream, salt, and pepper and cook, stirring, until cream is absorbed by mushrooms, about 1 minute. Transfer to a bowl and cool.
Make Mornay sauce while veal stands: Add enough milk to reserved veal juices to total 3 cups. Melt butter in a 2-quart heavy saucepan over moderately low heat, then add flour and cook over low heat, whisking constantly, 3 minutes. Add milk mixture in a stream, whisking, and bring to a boil, whisking. Reduce heat to low and gently simmer, whisking occasionally, 10 minutes. Remove from heat and add Gruyère, whisking until melted, then whisk in salt, pepper, and nutmeg.
Assemble veal Orloff: Move top rack to middle of oven and increase temperature to 375°F.
Stir 1/4 cup soubise into duxelles, then transfer remaining soubise to a sealable plastic bag. Transfer duxelles mixture to other sealable plastic bag, then seal each bag, squeezing out excess air. Snip off 3/4 inch from a bottom corner of each bag.
Remove string from veal, then trim off fat layer and ends of veal and discard. Cut roast crosswise into 16 slices (1/4 inch thick), keeping slices together. Transfer 1 slice of veal to end of ovenproof platter, then pipe about 1 1/2 tablespoons soubise onto half of slice, starting at bottom of slice and working toward top. Pipe about 1 1/2 tablespoons duxelles on other half of slice in same manner. Overlap with another slice of veal, leaving about 1/2 inch of stuffing exposed. Repeat with remaining veal slices and remaining soubise and duxelles, keeping slices aligned.
If necessary, heat Mornay sauce over low heat, stirring, until loose enough to spoon, then spoon 1/2 to 3/4 cup over top and sides of veal, covering slices and stuffings thinly but completely.
Bake veal Orloff, uncovered, until heated through and Mornay sauce glazes veal, 15 to 30 minutes.
Heat remaining Mornay sauce over moderate heat, stirring occasionally (thin with a little milk, if necessary), until hot and transfer to a gravy boat to serve on the side.
Cooks' notes: Veal can be braised (but not sliced) 1 day ahead and cooled, uncovered, then chilled, covered. Soubise, duxelles, and Mornay sauce can be made 1 day ahead. Cool soubise and duxelles, uncovered, then chill, covered. Cover surface of hot Mornay sauce with a round of wax or parchment paper, then cool slightly and chill. Veal Orloff can be assembled (without Mornay sauce) 4 hours ahead and chilled, covered with plastic wrap. Bring to room temperature before proceeding.