In a large pot over medium heat, cook the bacon, stirring occasionally, until crispy — about 8 to 10 minutes. Using a slotted spoon, transfer the bacon to a plate and set aside, leaving about ¼ cup of the bacon fat in the pot. Cut into bite-size pieces.

Add the onion, red or yellow pepper, jalapeños, garlic, and ½ teaspoon of salt to the pot. Cook over medium heat, stirring often, until the vegetables are softened, about 5 to 6 minutes.

Sprinkle the flour over the vegetables and stir until everything is evenly coated and forms a paste. Gradually whisk in the chicken broth and milk until smooth. Bring the mixture to a gentle boil, then reduce heat to medium-low. Simmer, stirring occasionally, until the soup has thickened slightly and reduced by about one-quarter, roughly 10 minutes.

Add the pieces of cream cheese and stir until it melts completely. Stir in the shredded chicken and three-quarters of the cooked bacon. Continue cooking until the chicken and bacon are heated through, about 1 minute.

Ladle soup into bowls and top with shredded cheddar and the remaining bacon. Garnish with extra jalapeño slices, if desired. Serve warm.