1-Gather and prepare all ingredients ahead of time for quick assembly, like shredding the chicken and chopping the veggies.

2-In a Dutch oven or soup pot, melt the 2 tablespoons unsalted butter with the 1 tablespoon olive oil over medium-high heat.

3-Add the 1 large finely chopped onion, 2 medium julienned carrots, ½ teaspoon salt, and 1 teaspoon fresh ground black pepper; cook for about 5 minutes until the onions soften.

4-Stir in the 3 tablespoons all-purpose flour to coat the vegetables and cook until a fond forms on the pan bottom.

5-Add the 3 cups low sodium chicken broth and scrape the pan to release the browned bits.

6-Pour in the 4 cups broccoli florets cut into ½-inch pieces; simmer covered over medium-low heat for 10 minutes.

7-Stir in the 2 cups half and half or milk, or 1 cup whole milk with 1 cup heavy cream, 8 ounces extra-sharp cheddar cheese shredded, and 4 ounces American cheese diced into cubes; cook until the cheeses melt.

8-Add the 2 cooked chicken breasts poached or rotisserie (about 2 cups diced or shredded), cover, and simmer for 5 to 10 minutes until heated through.

9-Adjust seasoning with salt and pepper, garnish with additional shredded cheddar cheese and fresh cracked black pepper, and serve with crusty bread.