1 pound spaghetti
6 tablespoons butter, divided
3 garlic cloves, minced
1 pound mushrooms (such as button or cremini), sliced
3 tablespoons flour
1 tablespoon chopped fresh thyme
2 cups whole milk
Kosher salt
Freshly ground black pepper
3 tablespoons olive oil
1/2 cup freshly grated Parmesan cheese
1/4 cup chopped flat-leaf parsley
Cook the pasta according to the package directions, reserving 1 cup of the cooking water before draining.
In a large skillet over medium-high heat, melt 3 tablespoons of the butter.
Add the garlic and mushrooms and cook, stirring frequently, until the mushrooms are softened and golden brown, about 8 minutes. Remove the mushrooms from the pan.
Add the remaining 3 tablespoons of butter to the pan and melt again over medium-high heat.
Put in the flour and thyme and cook, whisking constantly, until the flour turns very light golden brown, about 4 minutes.
Whisking continuously, add the milk in a slow stream and simmer for about 2 minutes, until the sauce thickens. Season with salt and pepper to taste.
Add the cooked pasta to the sauce along with the mushrooms and olive oil. Mix well and heat through, adding the reserved pasta cooking water, a little at a time, if necessary to achieve the right sauce consistency.
Serve hot, garnished with Parmesan cheese and chopped parsley.