Cook bacon in a large skillet until crisp. Transfer to a plate lined with paper towel. Pour off most of the fat and leave about 2 teaspoons in the pan.
Bring a large pot of salted water to a boil. Cook orecchiette until al dente. Drain and set aside.
Add butter and mushrooms to the skillet over medium heat. Let them brown for 3 to 4 minutes without stirring. Flip the mushrooms. Add garlic and cook 3 to 4 minutes more.
Whisk cornstarch with half and half in a small bowl. Pour it into the skillet. Add milk, crumbled bacon, salt, pepper, thyme, and Parmesan. Stir until smooth.
Simmer on medium low. Stir now and then until the sauce thickens, about 6 to 8 minutes.
Add the cooked orecchiette. Toss until the pasta is coated and glossy. Taste and adjust seasoning, then serve hot.