Preheat oven to 350 degrees F. Using a dutch oven, saute sliced onions in 2 tablespoons of vegetable oil. Add about 1/2 teaspoon salt to the onions. Saute onions until they are translucent. Remove onions from pan.
Sprinkle both sides of the brisket with salt and pepper. Place brisket into pan and brown on both sides. Once brisket is browned on both sides, remove brisket from pan.
Pour in the beef broth and scrape brown bits from the bottom of the pan. Add two tablespoons of tomato paste and whisk together well. Place onions and the brisket back into the pan, adding enough broth to the pan to cover the brisket half way.
Bake brisket for approximately 3 1/2 hours. The brisket is done when a fork slides into the meat easily. If the meat is still tough after the initial baking, bake for an additional 30 minutes. Once the brisket is removed from the oven, let rest for approximately 20 minutes before slicing. You can also chill, wrapped well in plastic wrap, until needed.
Prepare lasagna noodles as directed on the package. To use the noodles for the baked pasta dish, once the noodles are done, they need to be cut in half vertically, and horizontally.
Combine heavy cream and butter in a sauce pan over medium to medium high heat. Once the butter and cream just begin to simmer, whisk in all of the cheeses. The sauce will thicken. Once the cheeses have melted, remove pan from heat.
Place noodles into a 2 quart casserole dish. Arrange the noodles by folding them over so they make nice curls. Pour 3/4 of the sauce over the noodles. Toss spinach with olive olive, and then layer the spinach around the sides of the casserole dish.
Place 8 ounces of beef over the noodles. Top with remaining sauce and place back into the oven for 15 minutes, until the sauce starts to brown on the top of the pasta. If it hasn't started browning yet, stick under broiler for a minute or two.