Slice and season the chicken. Cut chicken into thin strips so it cooks quickly and stays tender. Coat with oil and spices until evenly covered.
Warm a skillet. Heat a large skillet over medium-high heat. You want it hot enough to sear, but not so hot that the spices burn.
Cook the chicken. Add the chicken in a single layer. Let it cook undisturbed for 2–3 minutes so you get a light golden color, then stir and finish cooking until no pink remains (about 6–8 minutes total).
Lower the heat. Reduce heat to medium-low. Push the chicken to one side of the skillet (or remove it briefly to a plate).
Melt the butter. Add butter to the empty side of the pan. Once it melts, stir in the minced garlic.
Let the garlic bloom. Cook garlic for 30–60 seconds, stirring often. You’re looking for a gentle sizzle and a deep aroma—not browning.
Build the creamy base. Add cream cheese and stir until it softens and starts to melt into the garlic butter. It will look a little messy at first; keep stirring.
Smooth it out. Stir in sour cream (or Greek yogurt). If the mixture seems too thick, add a splash of milk—just enough to make it creamy and spreadable.
Melt in the cheese. Add mozzarella, cheddar, and Parmesan. Stir until the cheese melts and the mixture looks glossy and cohesive. You should see gentle bubbling, not aggressive boiling.
Combine with chicken. Return the chicken to the sauce and toss until everything is coated. Finish with parsley and taste for salt and pepper.
Fill the tortillas. Spoon the filling down the center of each tortilla. Don’t overfill—too much makes wrapping difficult and can cause leaks.
Wrap and toast. Fold like a burrito (tuck sides in, then roll). Toast seam-side down in a clean skillet over medium heat for 1–2 minutes per side, until golden and lightly crisp. The outside should feel firm, and the inside should be hot and melty.