Bring a large pot of salted water to a boil, and cook the pasta to the package directions. About 1 minute before the pasta finishes cooking, add the broccoli florets to the pot. Drain the water, briefly rinse with cool water, set aside. While the pasta cooks, make the white sauce.
8 ounces short pasta noodles, 1 ½ cups broccoli florets
In a medium saucepan, melt the butter over low to medium heat. Add the flour and whisk to combine. The mixture should be smooth and free of lumps.
5 tablespoons unsalted butter, 5 tablespoons all-purpose flour
Add the whole milk, heavy cream, thyme, salt, and pepper. Continue to whisk until the ingredients are well combined. Add the mushrooms and reduce the heat to low. Use a wooden spoon to stir constantly until the sauce begins to thicken. Don't let it bubble or boil; otherwise, it will separate. It should be smooth and creamy in consistency. Remove from heat.
1 cup whole milk, 1 cup heavy cream, ½ teaspoon dried thyme, ½ teaspoon salt, ¼ teaspoon ground black pepper, 2 cups baby bella mushrooms
Pour the sauce over the cooked pasta noodles and blanched broccoli. Gently toss to combine.