Cook the pasta in boiling water until al dente. Just before the pasta is done, add the broccoli, then drain.
Heat a medium saucepan over low-medium heat. Melt the butter, then add the flour. Whisk to combine.
Add the whole milk, heavy cream, thyme, salt, and pepper. Whisk to combine. Next, add the mushrooms, and stir until the sauce thickens.
Pour the mushroom sauce over the noodles and broccoli. Stir to combine.
Serve hot with crusty bread or a side salad.
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