Preheat the oven to 350°F (175°C) and lightly grease a 9x13-inch baking dish. Set aside.
Heat a large skillet over medium-high heat. Add the ground beef and cook, breaking it apart, until browned and fully cooked, about 6–8 minutes. Transfer the beef to a bowl and leave any drippings in the skillet.
In the same skillet, melt the butter over medium heat. Add the onion, red bell pepper, and green bell pepper. Cook, stirring occasionally, until softened, about 5 minutes.
Meanwhile, bring a large pot of salted water to a boil. Cook the jumbo shells according to package directions until al dente. Drain and let cool slightly.
Return the cooked beef to the skillet with the vegetables. Stir in the Worcestershire sauce, ketchup, kosher salt, and ground black pepper until evenly combined. Remove from heat.
Stuff each cooked shell with the beef and pepper mixture and arrange the shells in the prepared baking dish.
Tear the provolone cheese slices into quarters. Place one quarter of a cheese slice on top of each stuffed shell.
In the same skillet, combine the milk, beef broth, and cornstarch over low heat. Stir continuously until the cornstarch dissolves and the sauce begins to thicken slightly, about 2–3 minutes.
Add the remaining provolone cheese and stir until fully melted and smooth.
Pour the cheese sauce evenly over the stuffed shells. Bake until the cheese is melted and bubbly, about 15 minutes. Let cool slightly before serving.