Place cream cheese in a microwave-safe bowl. Microwave on high power until soft, about 20 seconds. Stir in half-and-half until combined; set aside.
Heat oil in a large skillet over medium heat. Add bell peppers, jalapeños, and garlic; sauté until soft, 5 to 7 minutes. Stir in chicken, dried shallots, cayenne pepper, salt, and black pepper. Add cream cheese mixture, chicken stock, salsa, cumin, and oregano; bring to a boil.
Reduce heat; simmer for 1 to 2 hours.
