Step 1
Bring a large pot of salted water to a boil. Prepare a large bowl of ice water. If using regular broccoli, cut into 2-inch pieces. Trim broccoli di ciccio or broccolette but leave whole. Blanch broccoli until bright green and just tender, about 1 minute. Transfer to ice water to cool. Let drain and squeeze out extra moisture. Roughly chop broccoli into bite-size pieces.
Step 2
Mince 3 garlic cloves and halve the remaining one.
Step 3
Heat 2 tablespoons olive oil in a heavy-bottomed skillet over medium-high until hot but not smoking. Fry 2 pieces of bread until golden brown, about 2 minutes per side. Set bread aside. Repeat with 2 more tablespoons olive oil and remaining bread.
Step 4
Add remaining tablespoon oil to skillet. Add minced garlic, the anchovies and chile flakes, and cook for about 30 seconds or until fragrant. Add broccoli and heat until warmed through, 1 to 2 minutes. Turn off heat and stir in lemon juice and zest and a pinch of salt, or to taste.
Step 5
Rub fried bread with garlic clove halves and sprinkle with some of the cheese. Place broccoli on top of bread and garnish with more cheese.