Place a large skillet with a lid over medium-high heat. Cook the ground beef for 7-8 minutes or until cooked through, breaking into small pieces as it cooks. Remove the cooked ground beef to a bowl; set aside. 
Meanwhile, as the beef cooks, cook the pasta in a saucepan of boiling water according to the package directions. Drain and set aside. 
Wipe out the skillet from Step 1 and place it over medium-high heat. Add the oil, broccoli, onion, and garlic. Cook for 4-5 minutes or until the onions are translucent and tender.
Sprinkle the flour over top of the vegetable and stir to evenly coat the vegetables with the flour. 
Reduce heat to medium-low and slowly add the milk, one cup at a time, whisking constantly after each addition. Once all milk has been added and mixture has thickened, about 8 minutes, add the half-and-half, tomato paste, mustard, shredded cheese, Italian seasoning, paprika, salt, and pepper. Stir together until mixed. Remove from heat.
Add the cooked pasta and cooked ground beef to the skillet, carefully folding into the cheese sauce and veggies until evenly mixed. Serve warm.
Store leftovers in the fridge for up to 3 days.