Sauté the Vegetables
In a 4 or 5-quart Dutch oven or soup pot, add the diced onions, celery, green and red bell peppers, and chopped jalapenos. Sauté them over medium heat for about 5 minutes or until the peppers are just tender, stirring occasionally to ensure even cooking.

Add the Thickener
Sprinkle the 1/4 cup of all-purpose flour over the veggies, along with the minced garlic. Stir well constantly for about 1 minute. The mixture will become a little thick and pasty; this is normal and forms the base of the soup.

Add Liquids and Simmer
Increase the heat to medium-high. Pour in the chicken broth one cup at a time, incorporating each addition completely into the veggie mixture before adding the next to ensure a smooth consistency. Once the broth is incorporated, stir in the half-and-half. Let the soup come up to a gentle boil and cook for 5 minutes to thicken.

Temper the Cream Cheese
Place the softened cream cheese chunks in a medium heat-proof bowl. Slowly pour in about 1/2 cup of the hot broth mixture from the pot, whisking vigorously until the cream cheese is smooth and creamy. This prevents the soup from curdling.

Melt the Cheeses
Pour the smooth cream cheese mixture back into the soup pot. Add the shredded sharp cheddar cheese and stir continuously until all the cheese has melted into the broth.

Add Chicken and Finish
Stir in the cooked shredded chicken. Once the chicken is heated through, remove the pot from the heat.

Serve
Ladle the soup into bowls and garnish with toppings of your choice, such as fresh jalapeno slices, crushed croutons, or green onions.