Grate the cheese.
Mix together the tomato paste, oregano, garlic powder, and salt.
Press about 1/8th a pound of the hamburger into the burger press, using the smaller end to make an indentation into the burger.
In the indentation put about a tablespoon of shredded cheese, and a teaspoon of the tomato mixture into the center of each burger.
Top with another 1/8th pound of hamburger, flattened.
Remove the burger from the burger press and press the edges together firmly.
Preheat the grill to medium heat and grill the burgers over medium heat until they’re the the desired doneness.