Preheat a large skillet over medium-high heat. Add the olive oil, then the diced yellow onion. Cook until softened, about 5 minutes. Add the minced garlic and cook until fragrant, about 30 seconds. Push the aromatics aside and add the ground beef. Break up the meat with a wooden spoon and brown it thoroughly. Drain off any excess grease.

Reduce the heat to medium. Stir in the tomato paste, chili powder, cumin, smoked paprika, oregano, and cayenne if using. Toast these spices for about one minute until fragrant.

Pour in the beef broth and stir to scrape up browned bits. Stir in the chopped green olives if using. Bring to a gentle boil, then simmer uncovered for 5-7 minutes until liquid reduces and filling thickens. Season with salt and pepper.

Transfer filling to a bowl and cool in fridge for at least 15 minutes.

Preheat oven to 400°F (200°C) and line baking sheets with parchment. Place 2 tablespoons of cooled filling off-center on each disc. Fold dough over to form half-moon, press edges to seal, then crimp with fork or repulgue method.

Whisk 1 tablespoon water into beaten egg for egg wash. Brush over empanadas. Bake for 18-22 minutes until puffed and golden brown.

Cool slightly and serve warm with dipping sauces.