Mix the ranch dressing ingredients in a bowl with seasoning. Cover until needed.
To make the burgers, gently fry the onion in 1 tbsp oil with the oregano, cumin and paprika. When soft, transfer to a large bowl and cool. Add the beef, worcestershire sauce and season. Mix well and add just enough egg to bind the mixture. Form into 4 burgers about 2 cm thick. Chill until needed (you can make these a day ahead).
Grill the burgers over medium-hot coals, about 5-6 minutes each side for medium, 8-9 minutes for well-done. Split and lightly toast the burger buns.
Lay 2 lettuce leaves and a slice of tomato on the base of each bun. Add some dressing. Top with a burger, relish and gherkins.