Begin cooking the pasta according to package instructions. Proceed with the other steps as the pasta cooks. When the pasta is cooked al dente, drain the pasta and set aside in the pasta cooking pot while you finish cooking the beef.
Heat the olive oil in a large skillet. Stir in the onions and cook for a few minutes until the onion begins to soften.
Add the pepper and garlic, cook for a few more minutes.
Add the ground beef to the skillet, stir to combine with the veggies. Add salt and pepper to taste.
Stir the beef occasionally. After about 5 minutes, it will begin to brown. Stir in the broth at this time along with the spinach. Cook another 5 minutes until the broth is absorbed and the beef is cooked through.
When the beef is cooked, combine the beef and veggies with the cooked pasta. Stir in the goat cheese and Manchego cheese. Transfer the beef and pasta mixture to a casserole dish.
Spread the brie cheese evenly around the top of the beef and pasta mixture. Cover the casserole dish, and bake for 15 minutes.
Remove cover, and bake the cheesy beef casserole for another 5 minutes. Remove from oven, serve and enjoy with a glass of red wine from Côtes de Bordeaux.
I wrote the instructions putting cooking the pasta first as it flowed better that way. However, you can start to cook the veggies and beef before adding the pasta to the boiling water, in order to have the beef and pasta ready about the same time.