Melt butter in a large pot or deep skillet over medium; sauté garlic about 1 minute until fragrant.
Add broth, milk, salt, pepper, mustard powder, and garlic powder; bring to a gentle boil.
Stir in uncooked pasta; return to a boil, reduce heat to medium, and cook 8 minutes, stirring occasionally.
Add broccoli; cook another 4-5 minutes until pasta and broccoli are tender.
Off heat, stir in cheddar until completely melted and creamy.
Rest 2-3 minutes to thicken; sauce continues thickening as it stands.
Adjust seasoning to taste; serve hot with extra cheese if desired.