Heat the olive oil in a skillet over medium-high heat. Season the skirt steak with salt and pepper. Sear for 2-3 minutes on each side until browned. Add the minced garlic during the last minute of cooking. Remove from skillet and set aside.
Melt the butter in the same skillet over medium heat. Whisk the eggs in a bowl until slightly frothy, then pour into the skillet. Cook gently, stirring, until softly scrambled. Remove from heat and stir in the green chiles.
Preheat oven to 350°F (175°C). Place taco shells upright in a baking dish. Layer skirt steak at the bottom of each shell, followed by scrambled eggs. Top with pepper jack and cheddar cheese.
Bake in the preheated oven for 10-12 minutes, until the cheese is melted and bubbly.
Top with pico de gallo and cilantro. Serve with sour cream on the side. Enjoy warm!