Toss peppers, onions, 2 tablespoons of oil, 1 ½ teaspoons of chili powder, 1 ½ teaspoons of garlic powder, salt, and pepper to taste, ensuring strips are well coated.
Spread seasoned vegetables on the sheet pan.
Cut chicken breasts into strips lengthwise. If breasts are too thick, butterfly them for thinner pieces.
Toss the chicken strips with the remaining oil, chili powder, garlic powder, salt, and pepper in a bowl.
Put the baking sheet with the mixed vegetables in the preheated oven.
Remove the sheet pan from the oven and push vegetables to one side using a spatula or tongs, covering about half of the sheet pan.
Spread seasoned chicken strips over the other half of the sheet pan and return to the oven for about 20 more minutes, tossing chicken and vegetables for even cooking. Chicken strips should reach an internal temperature of 165°F (74°C), and vegetables should be tender but not mushy.
Transfer the peppers to one bowl and the chicken to another when cooked.
Sprinkle cilantro, cotija (if using), and fresh lime juice over the chicken.
Plate the arugula, layer on onions and peppers, then top with the tender chicken, and enjoy.