Braised Venison Shoulder with Mushroom Pierogi

Name: Braised Venison Shoulder with Mushroom Pierogi
Cuisine: European
Ingredients: 3 tbsp. vegetable oil; 1 (2–2 1/2-lb.) boneless venison shoulder, tied into a roast; Kosher salt and freshly ground black pepper; 8 stalks celery, finely chopped; 2 large yellow onions, finely chopped; 4 cloves garlic, finely chopped; 2 cups red wine; 4 cups veal or vegetable stock; 2 medium carrots, finely chopped; 12 sprigs flat-leaf parsley; 1 bunch thyme; 1 tbsp. Dijon mustard; 2 cups (9 oz.) all-purpose flour, plus more for dusting; 1⁄2 tsp. kosher salt, plus more; 3 large eggs; 1 1⁄2 tbsp. olive oil; 5 oz. shiitake mushrooms, stems removed, caps thinly sliced; 1⁄4 cup minced shallots; 1 1⁄2 cups (10 oz.) MitiCrema cheese or chèvre; 1⁄2 tsp. fresh lemon juice; Freshly ground black pepper; 2 tbsp. whole milk; 4 tbsp. unsalted butter; Thyme leaves, to garnish