01 -
Set an oven rack in the middle position and preheat to 200°C.
02 -
Trim the stalks from the broccoli and cut florets into 1/2 cm pieces. Cube the cream cheese and grate the cheddar and Parmesan cheeses. Mince the garlic cloves.
03 -
Bring a large pot of heavily salted water to a boil. Add cavatappi pasta and cook 2 minutes less than package instructions for al dente, about 6 minutes. In the final minute, stir in the broccoli florets. Drain both together.
04 -
Melt unsalted butter in the emptied pot over medium heat. Add minced garlic and cook, stirring, until fragrant, about 30 seconds. Whisk in all-purpose flour until blended and the mixture resembles wet sand, about 1 minute.
05 -
Gradually whisk in milk, continuing to blend until smooth. Bring to a boil, then lower heat to medium-low. Simmer and stir occasionally until the sauce coats the back of a spoon, 4-7 minutes.
06 -
Remove pot from heat. Add cream cheese, grated cheddar, half of the Parmesan, and kosher salt. Stir until cheeses are fully melted and sauce is velvety.
07 -
Add drained cavatappi and broccoli to the cheese sauce, folding gently to coat evenly.
08 -
Transfer mixture to a 33x23 cm baking dish and spread uniformly. Scatter remaining Parmesan over the surface. Bake until top is golden and sauce is bubbling, 15-20 minutes.