In a 4 or 5 quart Dutch oven or soup pot, cook bacon over medium heat until crisp. About 8 to 10 minutes. Transfer the bacon to a plate lined with paper towels. Drain the bacon grease, leaving about 3 tablespoons in the pot.
Add onions, celery, bell peppers and jalapenos. Saute about 5 minutes or until peppers are just tender, stirring occasionally.
Sprinkle the flour over the veggies, along with the garlic and stir. Things will become a little thick and pasty. That’s okay.
Increase heat to medium-high. Add the broth one cup at a time, incorporating each addition completely into the veggie mixture until the soup is smooth. Then add the half-and-half. Let the soup come up to a gentle boil and cook for five minutes.
Place cream cheese in a medium heat-proof bowl. Slowly pour in about 1/2 cup of the hot broth mixture, whisking until smooth and creamy.
Add the cream cheese mixture and the cheddar cheese into soup until melted.
Stir in the cooked chicken and the bacon, reserving about 1/4 cup of the bacon for topping the soup. Remove from heat.
Ladle into soup bowls and garnish with toppings of your choice, such as sliced jalapenos, crushed croutons, and more cheese.