Preheat oven to 350 degrees. Start heating a large pot of salted water on the stove.
Heat a large nonstick skillet over medium-high heat. Add olive oil to coat. Add beef, using a spatula or spoon to crumble it, and season with salt and pepper. After it begins to brown, stir in the sausage. Cook the beef and sausage to brown well. Remove to a bowl.
Add onion and more oil if needed to the hot pan. Season lightly with salt and pepper. Cook until softened, then add oregano, thyme, crushed red pepper flakes, and garlic, and cook stirring constantly one more minute. Stir in wine, broth, and tomato paste and boil for 3 minutes. Remove 1/3 cup of the sauce and set aside. Then add the reserved meat, sausage, and any juices to the pan and simmer, stirring occasionally for 15 minutes (the mixture will be thick). Taste and add salt or other seasonings if needed.
About 5 minutes before the meat mixture is done, cook the pasta, gently crushing the tagliatelle bundles so the noodles break into smaller (about 2-inch) pieces as you drop them into the boiling water. Cook according to the package directions until just al dente. Drain and immediately toss with the reserved 1/3 cup of sauce.
Lightly coat a 9-inch cast iron skillet with olive oil and heat on stovetop over high heat. When smoking hot, turn off the heat and add half the sauced noodles (they should sizzle when they contact the pan). Lightly press them down and even the layer. Evenly spread the meat mixture over top, and then cover with remaining tagliatelle, gently pressing down. Lightly brush the top of the pasta with olive oil and sprinkle with black pepper. Bake 30 to 40 minutes or until nicely browned and crusty on top and bottom. Using a heavy-duty oven mitt, carefully remove the pan from oven. Let cool 10 minutes. Spoon servings right out of the pan.