1. In a large pot over medium heat, melt 4 Tbsp butter, then add the onion. Cook, stirring occasionally, for 3-5 minutes, until the onion begins to soften.
2. Add the garlic and flour. Cook, stirring, for 1 minute, then gradually add the chicken stock 1 cup at a time, stirring to incorporate after each addition.
3. Add the chicken and diced potato. Bring to a boil, then reduce heat to low, cover, and simmer for 15-18 minutes, until the chicken is cooked through (internal temp reaches 165F). Remove the chicken to a plate and let cool.
4. Add the milk, salt, pepper, nutmeg, cayenne, and broccoli. Bring to a boil, then reduce heat to low and simmer 5 minutes, stirring occasionally, until the broccoli is tender. Push some of the potatoes against the side of the pot with the back of a wooden spoon to encourage them to break down. Meanwhile, shred the chicken with your fingers or two forks.
5. Turn off heat and stir in the 3 cups of cheddar cheese and shredded chicken. Cover to keep warm.
6. For the Crispy Cheese Toast: Butter one side of each slice of sourdough. Heat a nonstick skillet over medium heat and sprinkle a thin, even layer of shredded cheddar onto the pan, about the same size as one slice of bread. Working one slice at a time, place the bread butter-side up on the cheese and cook until the cheese is golden and crisp, about 1-2 minutes. Carefully slide a spatula under the toast, flip, and cook the other side for 1-2 minutes, until golden brown and crisp. Cut the toast into smaller pieces, and serve with the soup. Enjoy!
