In a mixing bowl or resealable plastic bag, combine 2 tablespoons of the cooking oil, minced garlic, ground cilantro, ground cumin, cayenne pepper, dried oregano, and kosher salt to make a marinade.
Add the chicken breasts to the bag or bowl and coat thoroughly with the marinade; refrigerate while you prepare the vegetables (or marinate 20–30 minutes up to 2 hours if desired).
Heat the remaining 1 tablespoon of oil in a cast-iron skillet over medium-high heat.
Add the sliced onions and bell peppers to the hot skillet and cook, stirring occasionally, 7–10 minutes until softened and slightly browned; remove the vegetables and set aside.
Add the marinated chicken to the skillet and pan-fry 5–7 minutes per side, until golden brown and cooked through (no pink inside).
Remove the chicken and let it rest 5 minutes, then slice into strips.
Return the vegetables to the skillet briefly to rewarm, then add the sliced chicken and toss to combine. Adjust seasoning and add fresh lime juice to taste.
Warm the tortillas and serve the chicken and vegetables in the tortillas.
