Bring salted water to a rolling boil, add pasta, and cook until al dente (8–10 minutes). Drain well and set aside.

Place broccoli florets in a steamer basket over boiling pasta water, then cover and steam until bright green and tender-crisp, about 3 minutes.

Heat olive oil over medium heat in a skillet, add minced garlic, and sauté until fragrant and just golden, about 1 minute.

In the same skillet over medium heat, melt butter until foaming and golden around edges, about 1 minute.

Sprinkle flour into butter, whisking constantly to form a smooth roux, cooking for 1–2 minutes without browning.

Slowly pour in milk, whisking vigorously to avoid lumps, then simmer until sauce thickens and coats the back of a spoon, about 3 minutes.

Remove skillet from heat, add cheddar and Parmesan cheese, then stir until fully melted and the sauce is silky smooth.

Add drained pasta and steamed broccoli to the sauce, gently toss to coat every piece in rich, velvety cheese.

Taste the pasta and adjust seasoning with sea salt, freshly cracked black pepper, and red pepper flakes.

Divide into bowls, sprinkle with chopped fresh parsley, and serve immediately for maximum creaminess and color contrast.