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

Let this mixture sit for about 10 minutes.

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

Make a slight indentation in the center of each patty.

Heat olive oil in a skillet over medium-high heat.

Cook patties for 4-5 minutes on one side, then flip and cook for another 4-5 minutes.

Remove the patties from the skillet and keep warm.

In the same skillet, reduce heat and add minced garlic, sauté for 30 seconds.

Add tomato paste and cook for 2 minutes until caramelized.

Pour in heavy cream and mix well.

Add crumbled feta and smoked paprika to the sauce.

Stir constantly for about 3-5 minutes until the sauce thickens.

Return the cooked patties to the skillet and spoon sauce over each.

Simmer together for 1-2 minutes.

Plate the burgers with sauce drizzled over them.

Garnish with parsley and extra feta. Serve hot.