In a large skillet over medium heat, add the ground beef. Cook until browned, breaking it up with a wooden spoon as it cooks, about 5-7 minutes. Drain any excess grease.
Add the chopped red onion and minced garlic to the skillet. Cook for an additional 3-4 minutes, stirring occasionally, until the onion becomes translucent and fragrant.
Pour in the can of tomato sauce and sprinkle in the dried oregano. Stir well to combine all the ingredients, then reduce the heat to low. Let the mixture simmer for about 10 minutes, allowing the flavors to meld together.
While the meat mixture simmers, toast the kaiser rolls until golden brown to add a nice crunch and help hold the filling.
To assemble, place a generous scoop of the beef mixture onto the bottom half of each toasted roll. Top with a handful of chopped Romaine lettuce and a sprinkle of crumbled feta cheese. Finish with the top half of the roll.
Serve your Greek Sloppy Joes immediately while they are warm, and enjoy the explosion of flavors!