Cheesy Mushroom Baked Eggs for Two

Name: Cheesy Mushroom Baked Eggs for Two
Ingredients: 2 tablespoons unsalted butter; 3½ oz (100 g) shiitake mushrooms (or any mushrooms you like), wiped clean and coarsely chopped (about 1½ to 2 cups); 1 pinch sea salt; 1 pinch black pepper; 1 large clove garlic, crushed; ¼ teaspoon dried thyme leaves or ¾ teaspoon minced fresh thyme leaves; 1½ tablespoons heavy cream; 1½ oz (40 g) Emmental cheese (or any Swiss cheese you like), shredded (about ⅓ cup); 2 large eggs; 2 teaspoons minced fresh parsley leaves, for garnish; Toast, for serving (optional)