Preheat the oven to 450 degrees F. Bring a large pot of salted water to a boil. Add the pasta and cook as the label directs, then drain and set aside (reserve the pot).
Meanwhile, toss the broccoli on a baking sheet with 1 tablespoon olive oil, the parmesan and garlic. Transfer to the oven and roast until the broccoli is slightly charred and the cheese starts browning, about 12 minutes.
Melt the butter in the reserved pasta pot over medium heat. Whisk in the flour; cook, whisking, until lightly toasted, about 2 minutes. Add the mustard and milk and cook, whisking occasionally, until thick and creamy, 4 to 5 minutes. Whisk in the cheddar and season with salt and pepper; continue cooking until the cheese is melted, 1 to 2 more minutes. Stir in the pasta until coated and warmed through, about 1 minute.
Thread the mozzarella and tomatoes onto 8 small skewers. Drizzle with olive oil and season with salt and pepper. Serve with the pasta and broccoli.