Savory Bread Pudding with Wild Mushrooms and Bacon

Name: Savory Bread Pudding with Wild Mushrooms and Bacon
Ingredients: Unsalted butter for the dish; 1/2 lb. (225 g) country-style bread, preferably day-old; 1/2 lb. (225 g) thick-cut bacon, cut into 1/4-inch (6-mm) pieces; 2 small or 1 large leek, white and light green portions, sliced 1/2-inch (12-mm) thick; 2 Tbs. olive oil, as needed; 1 lb. (455 g) mixed wild mushrooms, sliced 1/4-inch (6 mm) thick; 1/2 cup (50 g) grated Parmesan cheese; 1/3 cup (7 g) fresh flat-leaf parsley, chopped; 2 tsp. fresh thyme leaves; 1/2 tsp. sea salt; 6 large eggs; 2 cups (480 ml) whole milk; 1 cup (240 ml) heavy cream; 1/4 cup (25 g) grated Gruyère, Comté or other firm cheese; Freshly ground pepper