Add a generous coating of olive oil to a preheated cast-iron pan over medium-high heat.
Add the broccoli (try to arrange the cut sides down), season with salt, and let cook, undisturbed, until the undersides are dark brown and the florets are bright green, about 4 to 5 minutes.
Toss everything around and let the broccoli cook a few minutes longer, until the new undersides take on some color and the stems are crisp-tender, another 5 minutes or so.
Crumble the cheddar cheese into ½” pieces and sprinkle them over the broccoli.
Let the cheese melt and bubble, creating crispy cheese sheets.
Once the cheese has softened and started to melt, and the cheese on the pan is golden brown and bubbling, the dish is done.
Serve with a pinch of crushed red pepper flakes and lemon wedges to squeeze over top.
