In a large bowl, mix the ground beef, crumbled feta cheese, minced garlic, dried oregano, salt, and pepper until just combined. Avoid overmixing to keep the burgers tender.

Divide the mixture into 4 equal portions. Gently shape each portion into patties, making a slight indentation in the center for even cooking.

In a large skillet, heat the olive oil over medium-high heat. Ensure the oil is shimmering but not smoking.

Carefully add the burger patties to the skillet. Cook for about 4–5 minutes on each side until browned and cooked to your liking. Remove from the skillet and set aside.

In the same skillet, add the canned crushed tomatoes, heavy cream, Italian seasoning, salt, and pepper. Stir to combine and let the flavors meld together.

Bring the mixture to a simmer, cooking for approximately 5 minutes. Stir occasionally until heated through and the sauce thickens slightly.

Place the cooked feta burgers on plates and generously spoon the rich tomato cream sauce over the top.

If desired, sprinkle fresh basil on top for a burst of color and flavor before serving.