Heat olive oil in large skillet over medium-high heat. Cook red bell pepper, onions and tomatoes together until onions are soft. Sprinkle with oregano and set aside.
Set the EGG for direct cooking (no convEGGtor) at 600°F/316°C.
Grill steaks to desired temperature, then slice into thin pieces.
Divide pizza dough in half and roll each half out into a circle, getting it as thin as possible.
Set EGG for indirect cooking (with convEGGtor) at 450°F/232°C. Make sure EGG grid is clean and gently lay each crust onto the grid. Cook about 1 to 2 minutes per side, depending on temperature of EGG. Use tongs to flip and cook each side of the crust. If bubbles appear, just prick the dough bubble and keep cooking.
Spread 1 tablespoon of paste on each crust. Divide and top each pizza with the tomato mixture, beef and cheese. Carefully return pizza to grill, lower heat and close grill lid. Cook an additional 3 to 4 minutes until cheese is melted. Keep close watch on pizzas, removing if the crust is getting toasty. If you like a little bit of char on the bottom of the pizza – this is what gives it some authentic flavor.
Sprinkle with the 1⁄4 cup tomatoes that were set aside along with the fresh parsley. Serve immediately.
Makes 2 pizzas.