Georgian Funeral Rice

Name: Georgian Funeral Rice
Ingredients: 2 Tbsp. vegetable oil; 12 oz. boneless lamb leg or loin (see footnote), trimmed and cut into ½-in. chunks; 2 tsp. kosher salt, plus more to taste; 1 large onion, finely chopped; 1½ cups short-grain rice such as Carnaroli or arborio; 1 Tbsp. plus 1 tsp. caraway seeds, finely ground; 1 Tbsp. freshly ground black pepper, plus more for garnish; 1 tsp. dill seeds (optional); ¾ cup dry wine (red or white); 3¼ cups lamb, beef, or chicken stock, or water, divided; 1 bay leaf; 3 Tbsp. unsalted butter, at room temperature; 1 cup coarsely grated pecorino or other hard sheep’s-milk cheese, plus more for garnish