Place bacon in a large skillet and cook over medium-high heat, turning occasionally, until evenly browned, about 10 minutes. Drain bacon slices on paper towels.

While bacon is cooking, melt butter in a pot over medium-high heat. Add jalapeno peppers and garlic; cook until soft, 3 to 4 minutes. Add chicken broth, dried cilantro, Cajun seasoning, and onion powder; stir up any browned bits from the bottom of the pot. Bring to a boil. Reduce heat and add chicken. Simmer for 10 to 15 minutes.

Add cream cheese, most of the Cheddar cheese, and heavy cream; simmer, stirring occasionally, until cheese has dissolved, about 5 minutes. Season with salt and pepper.

Serve soup with remaining cheese. Crumble bacon on top.