In a large mixing bowl, combine the ground beef, crumbled feta, egg, finely chopped onion, minced garlic, oregano, salt, and pepper. Mix gently until just combined.

Divide the mixture into four equal portions and shape each into thick patties.

Heat a skillet over medium-high heat and drizzle with olive oil. Cook the patties for 4-5 minutes per side.

In the same skillet, lower the heat to medium and sauté minced garlic until fragrant. Add tomato paste and cook for 1 minute.

Pour in the heavy cream, stirring gradually. Add remaining crumbled feta and smoked paprika, mix well, and cook for 3-5 minutes.

Return the cooked patties to the skillet with the sauce and heat through for 1-2 minutes.

Plate the burgers, drizzle with extra sauce, and garnish with parsley, feta, and smoked paprika. Serve hot.