Wild Mushroom Crêpes with Sunny Eggs

Name: Wild Mushroom Crêpes with Sunny Eggs
Ingredients: 2 tablespoons unsalted butter; 10 ounces wild mushrooms, such as hen-of-the-woods or oyster, torn into bite-size pieces; 1 teaspoon finely chopped thyme, plus more for garnish; 1 garlic clove, thinly sliced; 1 tablespoon finely chopped parsley; Sea salt; Pepper; 1 tablespoon unsalted butter; 1 tablespoon all-purpose flour; 1 cup heavy cream, divided; 1/4 teaspoon freshly grated nutmeg; 8 large eggs, divided; 1 cup whole milk; 1 cup bread flour; 1 tablespoon unsalted butter, melted, plus more for brushing; 1 teaspoon kosher salt; Mesclun, for serving