3 tablespoons unsalted butter
1 large onion, chopped medium (about 1 1/2 cups)
4 medium carrots, peeled and chopped medium (about 2 cups)
3 large ribs celery, chopped medium (about 2 cups)
1 medium Garlic clove, minced (about 1 tsp.)
2 large bay leafs
2 teaspoons Fresh thyme, minced or 3/4 tsp. dried
2 lbs leeks (about 4 medium), white and light green parts, , halved lengthwise, cleaned thoroughly, and cut into 1-inch pieces (about 7 cups)
2 lbs medium red-, yellow-, or white-skinned potatoes (about 5 medium), peeled and cut into 3/4-inch cubes (about 6 cups)
3 cups low-sodium chicken broth
2 cups half-and-half
8 oz smoked cheddar cheese, grated (about 3 cups)
1/2 teaspoon kosher salt, or to taste
1 teaspoon freshly ground black pepper, or to taste
2 teaspoons snipped chives, for garnish (optional)