Preheat oven to 350 degrees F. Grease a 9-inch pie plate with olive oil and place it on a foil-lined baking sheet (to catch any drips while baking).
In a large mixing bowl, whisk the eggs. Whisk in the kosher salt, garlic powder, onion powder, dried oregano and cayenne.
Whisk in the Dijon mustard and the tomato paste. Set the egg mixture aside.
Heat a large stainless steel skillet over medium heat. You can add some oil if you want, but I find it unnecessary as the beef releases quite a bit of fat. Add the ground beef and cook, stirring often and breaking it up as it cooks, until no longer raw but still slightly pink, about 5 minutes. Drain. Allow to slightly cool.
Mix the cooked and drained ground beef into the egg mixture. Mix in 1 cup shredded cheddar.
Transfer the mixture to the prepared pie plate, packing it in and smoothing the top and sides out. Sprinkle the remaining 1/2 cup cheddar on top.
Bake until set, about 30 minutes. Let cool in the pan for 15-20 minutes before slicing and serving.