Fill an 8-qt. pot with 4 qts. water and add 1/2 cup kosher salt (this may seem salty, but it will season the broccoli perfectly). Bring to a boil. While water heats, cut broccoli heads into similar-size clusters of 3 or 4 florets plus stems. Add broccoli clusters to pot and cook, covered, just until bright green, 3 to 4 minutes. Drain broccoli and spread out on a towel-lined rimmed baking sheet to cool and dry off.
Heat a charcoal or gas grill to high (550° to 600°). If broccoli is still wet, pat dry, then grill until lightly charred on all sides, turning often, about 5 minutes. Let sit at room temperature for up to 2 hours, or chill up to 1 day.
Just before serving, put broccoli in a large bowl and toss with lemon juice, oil, chile flakes, salt, and pepper. Taste and adjust seasonings if you like. Transfer to a large serving bowl or platter and serve hot or at room temperature.
Make ahead: Through step 1 or 2, up to 1 day, covered and chilled. Let come to room temperature before proceeding with step 3.