Cream of Wild Mushroom Soup

Name: Cream of Wild Mushroom Soup
Ingredients: 5 ounces fresh shiitake mushrooms; 5 ounces fresh portobello mushrooms; 5 ounces fresh cremini (or porcini) mushrooms; 1 tablespoon good olive oil; 1/4 pound (1 stick) plus 1 tablespoon unsalted butter, divided; 1 cup chopped yellow onion; 1 carrot, chopped; 1 sprig fresh thyme plus 1 teaspoon minced thyme leaves, divided; Kosher salt; Freshly ground black pepper; 2 cups chopped leeks, white and light green parts (2 leeks); 1/4 cup all-purpose flour; 1 cup dry white wine; 1 cup half-and-half; 1 cup heavy cream; 1/2 cup minced fresh flat-leaf parsley