1. In a large bowl, mix together the softened cream cheese, sour cream, drained green chiles, ground cumin, chili powder, garlic powder, onion powder, shredded cheddar cheese, shredded pepper jack cheese, and diced chicken. Season the mixture with kosher salt and fresh ground black pepper to taste.
2. Spoon the chicken and cheese mixture in a line across the top third of a tortilla. Roll the tortilla tightly around the filling and secure it with a toothpick.
3. Heat about 1 to 1 1/2 inches of vegetable oil in a cast iron skillet or a heavy pot like a Dutch oven. Using tongs, carefully add a few taquitos to the hot oil.
4. Fry the taquitos for approximately 3 minutes on each side or until they turn golden brown.
5. Work in batches, frying a few taquitos at a time, and remove them to a paper towel-lined plate or platter as they finish cooking.
6. Once fried, carefully remove the toothpicks from the taquitos before serving.
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