Mushrooms and Dumplings

Name: Mushrooms and Dumplings
Cook time: 50 min
Total time: 50 min
Cuisine: European, American
Ingredients: 3 tablespoons unsalted butter; 2 tablespoons extra-virgin olive oil; 2 medium leeks (1 pound), white and light green parts only, thinly sliced (2 cups); Kosher salt and black pepper; 3 garlic cloves, minced; 1 pound small white button or cremini mushrooms, quartered (5 1/2 cups); 8 ounces shiitake mushrooms, thinly sliced (about 3 cups); 2 carrots, thinly sliced (1 cup); 3 dried shiitake mushrooms, grated on a Microplane and stems discarded (1/3 cup); 1 tablespoon all-purpose flour; 4 cups mushroom broth; 3 thyme sprigs; 2 tablespoons heavy cream or whole milk; Chopped chives, for garnish; 1 1/2 cups/205 grams all-purpose flour; 1 1/2 teaspoons kosher salt (Diamond Crystal); 1/2 teaspoon baking powder; 1/4 teaspoon black pepper; 1/4 teaspoon baking soda; 1 large egg; 1/2 cup/120 grams whole milk; 3 tablespoons/45 grams butter, melted