Preheat the oven to 425°F. Arrange 3 to 4 cups broccoli florets in a single layer on a baking sheet.
Drizzle the broccoli with 1 to 2 tablespoons olive oil, season with kosher salt and pepper to taste, and toss to coat. Spread the florets back into a single layer.
Roast the broccoli for 15 to 20 minutes, until the edges just begin to turn golden brown.
While the broccoli roasts, brush or spray both sides of 4 sourdough bread slices with olive oil.
When the broccoli is done, remove the baking sheet from the oven and transfer the roasted broccoli to a plate or bowl. Place the oiled sourdough slices on the same baking sheet and return to the oven for 5 minutes, until the bread is lightly golden and toasty.
Remove the bread from the oven. Spread ½ cup pimento cheese evenly over the 4 toasted sourdough slices.
Divide the roasted broccoli evenly on top of the pimento-cheese–topped slices.
Sprinkle ½ cup freshly grated cheddar cheese evenly over the assembled slices and return the baking sheet to the oven. Bake 10 to 15 minutes, until the cheese is melted and golden.
Remove from the oven, finish with freshly cracked black pepper to taste, and serve.