Mushroom and Potato Gratin with Thyme and Parmesan

INGREDIENTS

• 1 Tbs. unsalted butter, plus more for greasing
• 1 1/2 cups heavy cream
• 1 garlic clove, thinly sliced
• 3 fresh thyme sprigs, plus 1 1/2 tsp. minced
• Sea salt and freshly ground pepper, to taste
• 2 lb. Yukon Gold potatoes
• 1 Tbs. extra-virgin olive oil
• 1 lb. mixed wild and cultivated mushrooms, woody stems removed, caps thinly sliced
• 4 Tbs. grated Parmigiano-Reggiano cheese