Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper. Leave the puff pastry sheets out to thaw according to package instructions.

Heat olive oil in a large skillet over medium-high heat. Add the diced Spanish chorizo and cook for 3-4 minutes until the oils release and the edges become crispy.

Add the diced chicken, onion, and red bell pepper to the skillet with the chorizo. Cook for 5-7 minutes, stirring occasionally, until the chicken is browned and the vegetables soften.

Stir in the minced garlic, smoked paprika, salt, and black pepper, cooking for about 30 seconds until highly fragrant. Add the tomato paste, sliced olives, and chicken broth, stirring well to combine.

Reduce the heat to low and let the filling simmer for 5 minutes until the liquid has thickened and coats the chicken. Remove from heat and allow the filling to cool slightly for 10 minutes.

Place one sheet of puff pastry onto the prepared baking sheet. Spoon the slightly cooled chicken and chorizo filling evenly over the pastry, leaving a 1-inch border around the edges.

Place the second puff pastry sheet on top of the filling. Crimp the edges tightly with a fork to seal the pie, and brush the entire top with the beaten egg wash for a beautiful golden finish.

Cut three small slits in the center of the top pastry to allow steam to escape. Bake in the preheated oven for 25-30 minutes until the crust is puffed, flaky, and deep golden brown, then let rest for 5 minutes before slicing and serving.