Bring a large pot of salted water to a boil and cook the pasta according to the package instructions until it's al dente.

Reserve 1 cup of pasta water before draining.

Heat the olive oil in a large skillet over medium heat and cook the minced garlic for 1-2 minutes, until fragrant.

Add the broccoli florets to the skillet and cook for 3-4 minutes, until they start to soften.

Add the heavy cream to the skillet and stir to combine, then bring the mixture to a simmer and let it cook for 2-3 minutes, until the cream has slightly thickened.

Stir in the Parmesan cheese until it's melted and well combined, then season with salt, pepper, basil, thyme, and red pepper flakes.

Add the cooked pasta to the skillet, tossing to combine with the broccoli and cream sauce, and add some reserved pasta water if the sauce seems too thick.