Warm the vegetable oil in a large skillet over medium heat, ensuring an even sheen across the surface.
Distribute the steak and diced onion in a single layer, then season with salt, pepper and onion powder; sauté 4–8 minutes per side until the meat browns lightly and cooks through.
Transfer the skillet from the heat and allow the steak to rest for 5 minutes while you prepare the griddle or a cast-iron skillet over medium-high heat.
Lay each tortilla on the hot surface; scatter a modest portion of both cheeses over half of each tortilla, spoon the steak-onion mixture on top, and cover with another sprinkle of cheese before folding into a crescent.
Toast each quesadilla 1–2 minutes until the underside turns golden, flip carefully, and brown the second side for another 1–2 minutes, watching closely to prevent scorching.
Slide the finished quesadillas onto a cutting board, slice into wedges, and serve immediately while the cheese is at its most luscious.