Put the cut broccoli into a mixing bowl. Add the mayonnaise and stir until all the broccoli is thoroughly coated.
Season with salt, black pepper, lemon juice, and red-pepper flakes.
(Method 1: grilled) Preheat your grill so you have one hot side and one cooler side. Use tongs to place the broccoli onto the grill on the hot side. Cook, turning often, until the broccoli begins to char, about 2 to 3 minutes. Move the broccoli over to a less hot spot, close the lid and let it cook about 1 to 2 minutes. Move the broccoli to the cooler side of the grill, placing it on a piece of aluminum foil. Cover and continue to cook until it reaches desired doneness.
(Method 2: sautéed) Cook the broccoli in a skillet or cast iron pan.
Serve as a side dish or toss into lettuce, grain, or pasta salad.
