Heat a drizzle of EVOO in a small skillet over medium-high heat. Add 1/2 pound beef and brown and crumble. Season with salt, pepper, chili powder, paprika, cumin and coriander. Add chopped onion and garlic, and cook 2-3 minutes to soften. Add tomato paste and stock, and simmer to thicken and combine flavors, 15-20 minutes.
Bring potatoes to boil, salt the water and boil them for 3-4 minutes; drain. Heat about 1/4 cup EVOO in a sauté pan for shallow frying. Fry sliced potatoes until very crisp like fat potato chips. Remove to paper towels to drain and season with salt.
Combine remaining pound of ground beef with grated onion, Worcestershire, salt and pepper. Form 4 patties that are thicker at edges and thinner at the center for even cooking.