Lazy Cabbage Rolls

Name: Lazy Cabbage Rolls
Ingredients: 5 Tbsp. unsalted butter, cut into pieces; 3 small carrots, peeled, coarsely grated; 1 large onion, finely chopped; 3 garlic cloves, finely chopped; ½ small head of green cabbage (about 1 lb.), finely chopped; 1 Tbsp. plus 4 tsp. Diamond Crystal or 1 Tbsp. plus 1¼ tsp. Morton kosher salt, divided; 1 lb. ground pork; 2 cups cooled cooked long-grain white rice (such as jasmine or basmati); 4 tsp. paprika, divided; 1 tsp. freshly ground pepper; 1 tsp. crushed red pepper flakes, divided; 1 (24-oz.) bottle tomato purée or passata; Sour cream and coarsely chopped dill (for serving); Flaky sea salt; Warm sourdough bread (for serving)