2 tablespoons butter
1 onion, diced
3 garlic cloves, minced
1 teaspoon kosher salt
½ teaspoon freshly ground black pepper
¼ cup dry white wine
8 cups chicken broth, divided
4 ounces cream cheese, cut into small pieces
1 pound cooked chicken, shredded or diced
2 tablespoons Dijon mustard
2 tablespoons cornstarch
3 cups broccoli florets
2 cups shredded sharp cheddar cheese
Melt the butter in a stockpot or 6-quart Dutch oven over medium-high heat.
Add the onions and garlic. Cook, stirring frequently, until beginning to soften, about 3 minutes.
Stir in the salt, pepper and wine. Cook for 1 minute more. Add about ½ cup broth, the mustard, and the cream cheese. Whisk until the cream cheese has melted and is mostly incorporated.
Add the remaining broth and the broccoli, and bring to a simmer. Cook, uncovered, until the broccoli is tender, about 10 minutes. Puree using an immersion blender or in a countertop blender, if desired, and then return to a simmer.
Add the chicken and cheddar cheese. Heat, stirring, until the cheese is melted and the chicken is heated through. If you'd like the soup to be thicker, mix the cornstarch with an equal amount of cold water and whisk it into the hot soup. Serve hot.