Preheat your oven to 425 degrees.
Toss the broccoli and garlic cloves in a bowl with the olive oil, 1/4 tsp salt, 1/4 tsp pepper.
Arrange broccoli on a foil lined baking sheet and roast for 15 minutes.
Meanwhile, bring a pot of salted water to a boil on the stove. Add the pasta and cook until al dente.
Combine the butter and milk in a large skillet over medium high heat. Stir constantly until the butter is melted. Remove from heat and allow to cool slightly.
Drain the cooked pasta and add it to the skillet with butter and milk.
Reheat the skillet to medium high heat.
Stirring constantly, mix the whipping cream and Parmesan cheese into the skillet with the pasta. Continue to stir and bring to a boil.
Once boiling, mix in the broccoli and remove from heat.
Top with remaining 1/4 tsp salt and 1/4 tsp pepper.
Serve with additional Parmesan cheese, if desired.