Heat the oil in a 10-inch high-sided skillet over medium-high heat until shimmering. Add the onion and 1/2 teaspoon of the salt, and sauté until beginning to brown and soften, about 5 minutes. Stir in the bell pepper and garlic, and cook for 2 to 3 minutes until bell peppers begin to soften and garlic is fragrant. Add the ground chuck, pepper, and remaining 1/2 teaspoon salt. Cook, breaking up the meat into small pieces with a wooden spoon, until browned and no pink remains, 5 to 7 minutes.

Stir the pasta into the beef and onion mixture. Pour in the chicken broth, cover, and bring to a boil. Uncover and cook for 20 to 25 minutes, stirring occasionally, until the pasta is cooked and most of the liquid is absorbed. Meanwhile, arrange a rack in the middle of the oven and heat the broiler to high.

Stir half of the grated provolone and pepper jack cheeses into the pasta. Sprinkle the remaining cheese over the top. Broil until cheese melts and turns golden-brown, 2 to 3 minutes.