In a large skillet, heat 2 tablespoons of olive oil over medium-high heat. Add the diced chicken and season with salt and pepper. Cook until golden brown and cooked through, about 5-6 minutes. Transfer to a plate and set aside.

In the same skillet, add the remaining 2 tablespoons of olive oil. Add the diced onions and poblano peppers. Sauté until softened, about 4-5 minutes. Add the minced garlic and cook for another 30 seconds until fragrant.

Return the cooked chicken to the skillet. Add the drained diced tomatoes, cumin, oregano, smoked paprika, and cayenne pepper. Stir to combine and cook for 2-3 minutes to blend the flavors.

Remove from heat and stir in the chopped cilantro. Allow the filling to cool completely, at least 1 hour. For best results, refrigerate the filling for 2 hours or overnight to let the flavors develop.

Preheat your oven to 375°F (190°C). Line two baking sheets with parchment paper.

Place the empanada dough discs on a lightly floured surface. Spoon about 2-3 tablespoons of filling onto the center of each disc, being careful not to overfill.

Fold the dough over to form a half-moon and press the edges firmly to seal. Use a fork to crimp the edges decoratively or use the traditional repulgue technique by folding and twisting the edge.

Transfer the empanadas to the prepared baking sheets. Brush each empanada with the beaten egg for a golden finish.

Bake for 20-25 minutes, or until the empanadas are golden brown and crispy. Allow to cool for 5 minutes before serving.