Cabbage Chowder

Name: Cabbage Chowder
Ingredients: 4 tbsp. butter, divided; 1 lb. andouille sausage, sliced into thin rounds; 1 medium yellow onion, chopped; 2 carrots, thinly sliced; 1 stalk celery, thinly sliced; 3 tbsp. all-purpose flour; 4 c. low-sodium chicken broth; 4 c. chopped green cabbage; 3 large Russet potatoes, peeled and cut into 1 cubes; 0.333 c. heavy cream; 2 tbsp. chopped fresh dill sprigs, plus more for serving