Make the Soup Base: In a large pot, melt the butter over medium heat. Add the onion and garlic. Sauté for 3–4 minutes until the onions are soft and translucent.
Add Broth & Cream: Stir in the chicken broth and milk (or heavy cream). Bring to a gentle simmer and let cook for 5–7 minutes.
Melt the Cheeses: Gradually add cream cheese, cheddar, and Monterey Jack, stirring until smooth and creamy.
Add Jalapeños & Protein: Stir in chopped jalapeños and cooked chicken. Season with salt and pepper. Taste and adjust heat — add more jalapeños or hot sauce if you like it fiery.
Make the Grilled Cheese Dippers: Butter one side of each bread slice. Place two slices, butter-side down, in a skillet. Top with shredded cheese, then cover with remaining bread (butter-side up). Cook until golden on both sides, flipping once. Cut into strips or triangles.
Serve & Garnish: Ladle soup into bowls, top with cilantro or green onions, and serve with warm grilled cheese dippers.