Crispy roasted mushroom cacio e pepe

Ingredients

• 1 1/2 lbs mixed mushrooms, cleaned and sliced
• 2 sprigs fresh thyme, leaves picked off stems
• 2 large shallots, sliced thinly
• 1/2 C olive oil
• 1/2 lb pasta of your choice
• 6 T butter
• 1/2 C parmesan cheese, grated plus more for topping
• parsley, chopped
• salt and pepper to taste