1. Preheat oven to 500 degrees, with racks in upper and lower thirds. On a lightly floured surface, roll out 1 dough half into a 14-inch oval. Transfer dough to a parchment-lined baking sheet and brush with 1 teaspoon oil. Repeat with remaining dough half. Bake until crusts are puffed and golden brown, about 14 minutes, piercing large air bubbles with a knife, if necessary, and rotating sheets halfway through.

2. Meanwhile, pat steak dry and season with salt and pepper. In a large cast-iron or other heavy skillet, heat 1 teaspoon oil over medium-high until almost smoking. Cook steak until medium-rare, 6 to 8 minutes, flipping once. Transfer to a cutting board, tent with foil, and let rest 10 minutes.

3. In skillet, heat 2 teaspoons oil over medium. Add onion and bell peppers and season with salt and pepper. Cover and cook, stirring occasionally, until beginning to soften, about 5 minutes. Uncover and cook until vegetables are crisp-tender and dark brown in spots, 8 minutes.

4. Thinly slice steak against grain. Top crusts with steak, vegetables, and cheese. Bake pizzas just until cheese is melted, 3 minutes. Sprinkle with parsley before serving.