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

Divide the mixture into four equal portions and shape each into patties about 1 inch thick.

Heat a skillet over medium-high heat and add olive oil. Cook the patties for 4-5 minutes on each side until browned.

Remove the patties and sauté minced garlic in the skillet for about 30 seconds until fragrant.

Stir in the tomato paste and cook for 1 minute, then gradually add heavy cream, stirring until smooth.

Mix in the feta cheese and smoked paprika, adjust seasoning, and simmer for 3-4 minutes.

Return the patties to the skillet and spoon the sauce over them, heating through for 1-2 minutes.

Serve the burgers plated with sauce, garnished with parsley and feta crumbles.