Heat olive oil in a medium skillet over medium heat.
Add garlic, shallot, thyme, red pepper flakes, and salt. Cook briefly.
Add mushrooms and cook 3 minutes until softened and browned.
Squeeze lemon juice over mushrooms and remove garlic cloves.
Meanwhile, boil salted water and cook pasta 1 minute less than package directions.
Reserve 1 1/2 cups pasta water before draining.
Return drained pasta to pot with butter, cream, 1 cup pasta water, and Grana Padano.
Toss and cook over medium heat 2 minutes until sauce thickens and coats pasta.
Add more pasta water if needed to reach creamy consistency.
Fold in mushroom mixture and adjust salt.
Serve immediately with parsley and extra Grana Padano.