Combine ground beef, feta cheese, egg, chopped basil, minced garlic, and salt and pepper in a large mixing bowl.
Form the ground beef mixture into twelve equally sized patties.
In a large skillet over medium/high heat, cook the patties to desired temperature. I cook mine for about four minutes on each side before cutting into one to see if it needs a little more time. You may need to cook them in batches.
Using a slotted spatula, remove the patties from the pan and place on a paper towel-lined plate. Cover with foil to keep the burgers warm.
Drain the grease from the pan and lower the heat to medium/low. Add 2 Tablespoons of beef broth to the pan and whisk to deglaze, scraping any brown bits from the bottom of the pan.
Add one cup of heavy whipping cream, whisking well, then add Italian seasoning, green onions, and tomato paste. Whisk well.
Add salt and pepper to taste, then cook for about 5 minutes or until thickened.
Add the burger patties back to the pan, coat with sauce, then serve garnished with additional green onions if desired.
This recipe has 3 grams of net carbs per serving (2 patties).