Vegetarian Pot Pie

Name: Vegetarian Pot Pie
Ingredients: 5 tbsp. butter, divided; 12 oz. button mushrooms, quartered; 2 cloves garlic, chopped; 1 tsp. fresh thyme leaves; 2 carrots, chopped; 1 yellow onion, chopped; 3 celery stalks, chopped; 1/2 tsp. salt, plus more to taste; 1/2 tsp. ground black pepper, plus more to taste; 3 tbsp. all-purpose flour; 2 1/2 c. vegetable broth; 1/2 c. + 1 tablespoon heavy cream, divided; 1 15 oz. can white beans, drained and rinsed; 1 c. frozen peas; 1/2 c. freshly grated parmesan cheese, plus more for topping; 1 sheet puff pastry, from 1, 17oz package, thawed