Start boiling water: In a large pot, bring salted water to a boil. Add pasta and cook until almost al dente, about 2-3 minutes less than the package instructions. Add broccoli in the last minute of cooking.
Preheat oven: Set your oven to 375 degrees F to get it ready for baking.
Make roux for sauce: In a skillet over medium heat, melt butter. Whisk in flour until smooth, then add minced garlic and cook until fragrant.
Develop sauce: Gradually add milk, whisking constantly. Next, gradually add in the cheese. Cook until slightly thickened, then remove from heat. Season with mustard, salt, and pepper.
Combine: Mix the drained pasta and broccoli with the cheese sauce until well coated. Transfer to a baking dish if not using an oven-safe skillet.
Bake until bubbly: Top with breadcrumbs and bake for 15-20 minutes until golden and bubbling. Serve hot and enjoy your comforting meal!