Heat a Dutch oven or large stockpot over medium heat. Add the diced turkey ham and cook for about 5–7 minutes, stirring frequently, until lightly crisp. Transfer it to a paper towel-lined plate and reserve about 2 tablespoons of the cooking fat in the pot.
Add the chopped jalapenos, bell peppers, and onion. Sauté for 5–6 minutes, or until the vegetables begin to soften.
Stir in the minced garlic, flour, paprika, cumin, salt, and black pepper. Cook for about 1 minute, stirring constantly so the flour and spices coat the vegetables without burning.
Slowly pour in the chicken broth while stirring to prevent lumps. Bring the mixture to a gentle boil over medium-high heat.
Reduce the heat to medium-low. Add the cubed cream cheese and stir vigorously until completely melted and incorporated into the broth.
Pour in the half-and-half and add the shredded chicken. Stir well and simmer gently for about 10 minutes, until the chicken is heated through and the soup is creamy.
Taste and adjust the salt, pepper, or jalapenos if needed. This Jalapeno Popper Soup is best served hot.
Ladle into bowls and top with shredded cheddar, green onions, sliced jalapenos, and crumbled turkey ham, if desired.