In a mixing bowl, whisk together the flour and salt. Add the chilled butter cubes and quickly rub them into the flour with your fingertips or a pastry cutter until the mixture resembles coarse crumbs.
Gradually add ice-cold water, a tablespoon at a time, mixing gently until the dough just comes together. Knead lightly, then shape into a flat disk, wrap in plastic, and chill in the fridge for 20 minutes.
While the dough chills, heat a tablespoon of oil in a skillet over medium heat. Add the chopped onion and minced garlic; sauté until fragrant and golden, about 5 minutes.
Add the cooked ground beef or shredded chicken to the skillet, season with smoked paprika and cumin, then cook until heated through, about 8 minutes. Remove from heat and let cool slightly.
Preheat your oven to 200°C (390°F). Lightly flour a clean surface and your rolling pin. Roll out the chilled dough to about 3mm thickness, aiming for a 20cm square.
Use the round cutter to stamp out 8cm diameter circles from the dough. Reroll scraps if needed, but avoid overworking the dough.
Place about a teaspoon of filling in the center of each circle. Fold the dough over to form a half-moon shape and pinch the edges together, then crimp with a fork to seal.
Arrange the filled empanadas on a parchment-lined baking sheet. Brush the tops with beaten egg for a shiny finish.
Bake in the preheated oven for 20-25 minutes, until golden brown and crispy. The crust should crackle gently when done.
Remove from oven and let cool for 5 minutes. Serve warm or at room temperature, perhaps with a side of salsa or fresh herbs.
