If using broccolini, cut it into 2-inch segments. If using regular broccoli, peel the stems with a vegetable peeler first so that they cook evenly, then cut the rest into large chunks.
Pour about a 1-inch puddle of salted water into a large saute pan and bring to a boil. Add the broccoli and cover with a lid; let boil/steam for 2 minutes. Drain well and pat dry on paper towels, wringing out as much extra liquid as possible. Chop into small (roughly 1/2-inch) bits.
Wipe the saute pan dry and heat over medium. Add the olive oil and let it heat for a full minute. Add the garlic and pepper flakes, cooking until the garlic is just beginning to turn golden, about 1 minute. Add the broccoli and cook 1 to 2 minutes more, seasoning with salt. Transfer the mixture to a bowl and add the lemon zest and juice, Pecorino and more salt and pepper flakes to taste.
Preheat the broiler. Arrange the slices of bread on a baking sheet and lightly toast on both sides. Scoop the broccoli mixture onto each slice of bread, lay a slice of provolone over it and run under the broiler until the cheese has melted and begun to blister. Eat. Repeat. Don't forget to share, or at least hide the evidence if you decide not to.