Slice tenderloins lengthwise thinly in a spiral getting deeper and unrolling to flat about 1 cm thick. Precut butchers string and have it ready for tying rolls.
Stuffing: In a pan, melt 4 Tbl butter and sautee 1/2 cup onion, mushrooms, peppers and celery with the garlic at medium heat until soft. Stir in Parsley, Thyme, salt and pepper until combined and remove from heat.
Toast bread and let cool while mixing veggies for the stuffing then chop into cubes into a large bowl.
Toss cooled veggies and bread, adding drizzles of beef broth until bread is softened but not mushy. You may not need all of the broth.
On flat tenderloin, spread out stuffing evenly. Starting at which ever end is narrower, roll up to wider end, tucking stuffing in as needed. Tie snugly to contain roll and stuffing.
In a hot pan, melt 2 Tbl butter, brown outside of tenderloin rolls before laying in a baking pan. Mound any extra stuffing around and on top of rolls.
Preheat oven to 350.
Sauce: In a medium sauce pan melt 4 Tbl butter and add remaining veggies. Cook at medium - high heat until veg are tender then lower heat.
Stir in flour and continue to stir constantly for almost 2 minutes.
Whisk in warmed milk and continue stirring until mixture boils softly and has thickened, remove from the heat at this point and stir in cheese. Add salt and pepper to taste, stirring until cheese is blended then pour over stuffed rolls.
Blend breadcrumbs with remaining 2 Tbl melted butter and sprinkle over saucy tenderloin rolls.