Place the butter in a 4-quart soup pot and set over medium heat. Once the butter has melted, add the onions and garlic. Sauté for 3-4 minute, stirring to make sure the garlic doesn’t burn.
Place the whole chicken breasts at the bottom of the pot. Add the broth, sherry, Dijon mustard, corn starch, smoked paprika, crushed red pepper, 1 teaspoon salt, and 1/2 teaspoon ground black pepper.
Bring the broth to a boil. Lower the heat, cover, and simmer for 15-20 minutes to cook the chicken.
Remove the chicken breast with tongs. Then add in the cream cheese. Whisk to melt the cream cheese into the broth. Then use two forks to shred the chicken.
Add the broccoli florets and the shredded chicken to the soup. Stir well and turn off the heat. The small broccoli florets will cook quickly in the hot broth.
Taste, then salt and pepper as needed. Serve warm.