For the sauce: place the oil and garlic in a small saute pan on very low heat. Cook, turning occasionally until the garlic is golden brown all over and soft. Place the garlic and remaining ingredients for the sauce in a blender or food processor (add water as needed to smooth out the consistency) and blend until smooth. Season with salt and pepper to taste.
Preheat the oven broiler on high.
In a bowl mix the beef, Worcestershire sauce, cumin, salt, and pepper until fully combined. Place the mixture on a baking sheet and cover with plastic wrap. Using a rolling pin, roll the mixture to about 1/4 inch thick. (To test the flavor of the seasoning cook a small amount of the beef mixture in a saute pan)
Remove the plastic wrap and place under the broiler. Cook until nicely browned and somewhat crispy around the edges. (Be careful using the broiler to make sure it doesn't burn or scorch). Drain any excess grease into a jar or used can (not down the sink).
Warm the pita on both sides in a pan over medium heat for approximately 30 seconds per side.
Cut the beef into 1 inch wide strips to fit the pita.
Layer the pita with lettuce, beef, tomato, onion, sauce, and feta. Fold in half and serve with french fries and ketchup.