Warm and season the chicken. In a skillet over medium heat, add a teaspoon of oil. Toss in the chopped chicken and sprinkle over the bold seasoning mix. Stir until the chicken is coated and heated through, about 3–4 minutes.
Squeeze a little lime over it and set aside.
Sauté the aromatics. In the same pan, add a small drizzle of oil if needed. Cook the onion, bell pepper, and jalapeño with a pinch of salt until softened and lightly browned, 4–6 minutes. Stir the chicken back in to combine, then transfer everything to a bowl.
Scramble the eggs. Crack eggs into a bowl, add a pinch of salt and pepper, and whisk until smooth.
Melt 1 tablespoon butter in a nonstick skillet over medium-low heat. Pour in the eggs and gently push them around with a spatula, forming soft curds. Cook until just set but still glossy, 2–3 minutes.
Remove from heat.
Warm the tortillas. Heat tortillas one at a time in a dry skillet over medium heat for 15–20 seconds per side until pliable. Keep them covered with a clean towel so they stay soft.
Assemble the burritos. Lay a tortilla flat. Add a quarter of the chicken-pepper mixture down the center, leaving room at the edges.
Top with a quarter of the eggs, a generous handful of shredded cheese, a sprinkle of cilantro, and a few drops of hot sauce if you like. Fold the sides in, then roll tightly from the bottom up.
Toast the burritos. Wipe out the skillet and add a small dab of butter or oil. Place burritos seam-side down and cook over medium heat until golden and lightly crisp, 1–2 minutes per side.
This step seals the seam and melts the cheese.
Finish and serve. Slice in half if you want, add extra lime and salsa, and serve hot. For a heartier bite, add a spoonful of black beans or a strip of crispy hash browns before rolling.