The Night Before (or early in the day): Cook lasagna noodles in 6 qts. Boiling water for 5-7 minutes or until tender; drain, wipe noodles dry with a clean/dry cloth, lay flat on waxed paper.
While noodles are cooking, melt butter and olive oil in a large skillet. Saute onion, garlic and mushrooms until they're tender; add remove from heat; set aside.
Place cooked chicken in food processor and pulse until chicken resembles a tuna salad mixture. Combine chicken with the onions, garlic, mushrooms and the fat in which they were sauteed; add egg, cream and seasonings. Add spinach (cooked) and mix well.
Cut each lasagna noodle into 2 or 3 pieces-each piece should be 3 to 4 inches long; place a tablespoonful of the chicken filling on each piece and roll into a tubular shape. If you don't want to make canneloni, just layer the ingredients like you would for lasagna.
Arrange rolls next to each other, one layer deep, in a buttered baking dish; set aside while you prepare the cheese sauce.
Cheese Sauce: Melt butter then add the flour and cook for a few minutes to get rid of the floury taste. Gradually add the chicken broth, whisking constantly to prevent lumps; add cream, salt and pepper. Cook, stirring constantly, until thickened and smooth; remove from heat. Stir in 3/4 cup grated Parmesan cheese and mix well.
I like to use, both, red and white sauce on this one. I spoon over a strip of the white sauce, next to it I spoon on some red; keep doing that across the dish until the sauce covers the noodles. The red/white pattern makes it look pretty and gives the dish a little more flavor. It also cuts back on some of the fat.
Spoon sauce over cannelloni in baking dish; sprinkle with remaining Parmesan cheese and Mozzarella cheese, if used; refrigerate until you're ready to bake it.
Before Serving: Preheat broiler; place cannelloni 4-5 inches from heat and broil for 10 minutes or until sauce bubbles and top browns. If you'll be making lasagna, bake in a 350-degree oven for 25-30 minutes, or until it's bubbly and the top is browned a bit.