Creamy Clam Chowder

Name: Creamy Clam Chowder
Ingredients: 1/2 pound thick cut bacon slices (diced); 1 medium yellow onion (diced); 2 ribs celery (diced); 1 medium carrot (finely chopped); 2 tablespoons minced garlic; 1/3 cup all-purpose flour; 3 cups chicken broth; 2 cups half and half; 1 cup clam juice; 3 large russet potatoes (diced); 3 (6.5 ounce cans) clams ( in juices, chopped or minced); 1 teaspoon salt (or to taste); 1/2 teaspoon black pepper; 1/2 cup shredded cheddar cheese ((optional)); 1 tablespoon minced chives ((optional))