To make pasta dough in a food processor: Blend flour, eggs, salt, and water in processor until mixture just begins to form a ball, adding more water, drop by drop, if dough is too dry (dough should be firm and not sticky). Process dough for 15 seconds more to knead it. Transfer to a floured surface and let stand, covered with an inverted bowl, 1 hour to let the gluten relax and make rolling easier.
To make dough by hand: Mound flour on a work surface, preferably wooden, and make a well in center. Add eggs, salt, and water to well. With a fork, gently beat eggs and water until combined. Gradually stir in enough flour to form a paste, pulling in flour closest to egg mixture and being careful not to make an opening in outer wall of well. Knead remaining flour into mixture with your hands to form a dough, adding more water, drop by drop, if dough is too dry (dough should be firm and not sticky). Knead dough until smooth and elastic, 8 to 10 minutes. Cover with an inverted bowl and let stand 1 hour (to make rolling easier).
Make filling: Heat butter in a 12-inch heavy skillet over moderately high heat until foam subsides, then sauté onion, stirring occasionally, until golden, about 6 minutes. Add artichoke hearts and sauté, stirring occasionally, until tender, 8 to 10 minutes. Remove from heat and cool slightly.
Transfer all but 3/4 cup artichoke mixture to cleaned bowl of processor (reserve remaining artichoke mixture in skillet), then add cheese, parsley, yolk, lemon juice, salt, pepper, and nutmeg and pulse until mixture is coarsely chopped.
Roll pasta and make ravioli: Cut pasta dough into 4 pieces, then flatten each piece into a rough rectangle and cover rectangles with an inverted large bowl. Set rollers of pasta machine on widest setting.
Lightly dust 1 rectangle with flour and feed through rollers. (Keep remaining rectangles under bowl.) Fold rectangle in half and feed it, folded end first, through rollers 7 or 8 more times, folding it in half each time and feeding folded end through. Dust with flour if necessary to prevent sticking. Turn dial to next (narrower) setting and feed dough through rollers without folding. Continue to feed dough through rollers once at each setting, without folding, until you reach narrowest setting. Dough will be a smooth sheet (about 24 inches long and 4 inches wide).
Put sheet of dough on a floured work surface and drop 6 (1 1/2-teaspoon) mounds of filling 1 1/2 inches apart in a row down center of one half of sheet. Brush egg wash around each mound, then fold other half of sheet over filling. Press down firmly around each mound, forcing out air. (Air pockets increase the chance that ravioli will break during cooking.) Cut pasta (between mounds) with cutter into 3-inch rounds. Line a large shallow baking pan with a clean kitchen towel (not terry cloth) and dust towel with flour, then arrange ravioli in 1 layer in it. Make more ravioli with remaining pasta dough, 1 sheet at a time, and remaining filling, transferring ravioli to lined pan.
Put oven rack in middle position and preheat oven to 350°F. Lightly butter baking dish.
Bring a 6- to 8-quart pot of salted water to a boil. Add ravioli, carefully stirring to separate, and, adjusting heat to keep water at a gentle boil, cook until pasta is just tender, about 6 minutes. Transfer with a slotted spoon to a colander.
Assemble and bake dish: While ravioli boils, reheat reserved artichoke mixture in skillet with butter over moderately high heat, then add tomatoes and water and cook, stirring, until tomatoes are softened, about 5 minutes.
Transfer half of ravioli to baking dish and top with half of artichoke mixture, half of cream, and half of cheese. Repeat with remaining ravioli, artichoke mixture, cream, and cheese. Sprinkle with salt and pepper.
Bake, uncovered, until ravioli is heated through and cream is bubbling, about 15 minutes.
Dough can be made (but not rolled out) 4 hours ahead and chilled, tightly wrapped in plastic wrap. Ravioli can be made (but not cooked) 4 hours ahead and chilled in lined baking pan, covered.