Cheesy Broccoli Corn Potato Chowder with Ham

Name: Cheesy Broccoli Corn Potato Chowder with Ham
Ingredients: 1 16-ounce bag frozen corn; 1 pound Yukon gold potatoes, peeled and diced; 2 stalks celery, diced; 2 carrots, peeled and diced; 1/2 large yellow onion, diced; 2 cloves garlic, minced; 1/2 pound fresh broccoli florets; 1/2 teaspoon dried thyme; 1 teaspoon kosher salt, plus more to taste; 1/2 teaspoon black pepper, plus more to taste; 1 32-ounce carton low-sodium chicken or vegetable broth; 2 cups water; 2 cups shredded sharp cheddar cheese; 4 ounces Velveeta, diced; 1/2 cup heavy cream; 8 ounces ham, diced