Pound or slice the chicken breast into a 1/2-inch thick piece or 1/2-inch strips. In a shallow bowl, whisk together 1 tbs olive oil, 1 tbs lime juice, 1 tsp chili powder, 1 tsp cumin, 1 tsp garlic powder, 1 tsp smoked paprika, 3 tsp salt and 1/2 tsp black pepper. Add the chicken, turn to coat, and marinate at room temperature for 10–15 minutes (or up to 2 hours in the fridge).

Grill or sear the chicken

Heat a grill pan or skillet over medium-high heat until hot. Brush or wipe excess marinade from the chicken. Cook the chicken 3–4 minutes per side (for sliced strips, 2–3 minutes per side) until internal temperature reaches 165°F (74°C) and juices run clear. Transfer to a cutting board and let rest 5 minutes, then slice into thin strips about 1/4-inch wide.

For the fajita veggies

Slice vegetables

While the chicken rests, core and seed the bell peppers and slice into 1/4-inch strips. Peel and slice the onion into similar strips. Halve the jalapeño, remove seeds for milder heat (or keep some for more heat), and finely dice.

Sauté

Heat 1 tbs olive oil in a skillet over medium-high heat. Add the onion and peppers and cook, stirring occasionally, until softened and lightly charred at the edges, about 5–6 minutes. Add diced jalapeño, 1 tsp fajita seasoning, 1/4 tsp salt and 1/8 tsp black pepper; cook 1 more minute to bloom the spices. Transfer vegetables to a plate.

For the omelet

Beat eggs

In a bowl, whisk 3 large eggs with 1 tbs milk, 1/4 tsp salt and 1/8 tsp black pepper until frothy.

Cook omelet

Heat a nonstick skillet over medium-low and add 1 tbs butter, swirling to coat. Pour the egg mixture into the pan and let set undisturbed for 10–15 seconds, then gently pull the cooked edges toward the center with a spatula while tilting the pan so uncooked egg flows to the edges. Continue until eggs are mostly set but still slightly moist on top, 1½–2 minutes.

Add fillings and finish

Evenly distribute half of the sliced grilled chicken (about 3–4 oz), half of the sautéed peppers and onions, and 1/4 cup shredded cheddar jack cheese over one half of the omelet. Allow cheese to melt for 30–45 seconds, then carefully fold the omelet in half over the fillings and slide onto a plate. Sprinkle with chopped cilantro if using. Repeat the omelet process for a second omelet if serving more people or to use remaining fillings; otherwise reserve extra chicken and veggies for serving alongside.

To serve (optional)

Top the omelet with sliced avocado or a dollop of guacamole, a spoonful of sour cream or Greek yogurt, a squeeze of lime, and hot sauce if desired. Serve immediately while hot.