Jalapeño Popper Chicken Soup

Name: Jalapeño Popper Chicken Soup
Ingredients: 8 oz. bacon, cut into 1/2 pieces; 1 medium onion, finely chopped (about 1 1/2 c.); 1 large green bell pepper, seeded and chopped (about 1 1/4 c.); 4 jalapeños, seeded and finely chopped, plus sliced jalapeños for serving; 4 cloves garlic, minced; 1 tsp. kosher salt, divided; 1/4 c. all-purpose flour; 4 c. low-sodium chicken broth; 2 c. whole milk; 4 oz. cream cheese, cut into 1 pieces, room temperature; 2 c. cooked shredded chicken breast; 1 c. shredded cheddar