Spice-Rubbed Greek-Style Lamb Burgers - Fresh-Pressed Olive Oil

Ingredients

• 2 pounds well-chilled ground lamb, or 1 pound each ground lamb and ground beef
• 4 tablespoons extra virgin olive oil, divided use
• 2 tablespoons finely chopped fresh flat-leaf parsley
• 2 tablespoons finely chopped fresh dill
• 1 teaspoon finely chopped fresh oregano
• 1/2 teaspoon ground cumin
• 1/4 teaspoon smoked paprika
• 1/4 teaspoon sweet paprika
• 1/4 teaspoon onion powder, preferably toasted
• 2 cloves fresh garlic, peeled and finely grated or minced
• 1 1/2 teaspoon coarse salt (kosher or sea)
• Freshly ground black pepper to taste
• Pita bread or hamburger buns, for serving
• Crumbled feta cheese, for serving
• Tzatziki, for serving (optional; see below)