Preheat grill on high and reduce to medium when hot. Season steaks and grill to desired doneness. Move steaks to cutting board and rest for 3-5 minutes.
Unroll and cut pizza dough into four equal pieces. Press each piece to 1-1/2 times the original size and cut each piece in half. Brush with olive oil and grill about 2 minutes per side. Turn off flame for half of the grill (if using a charcoal grill, push coals to one side). Place grilled dough on the side without direct heat.
Thinly slice steaks. Top each dough piece with 1 ounce tomato basil sauce, 4 ounces steak, 1 ounce blue cheese and 2 ounces mozzarella cheese. Shut grill lid 3-4 minutes for cheese to melt; serve.