Heat a dual-contact electric grill, a grill pan, or an outdoor grill to medium-high heat.
Meanwhile, on a large platter, drizzle the broccolini with olive oil and sprinkle it with kosher salt, black pepper, and garlic powder.
Use your hands to toss everything together until the broccolini is well-coated.
Grill the broccolini, turning it often, until the stalks are tender-crisp and the tops are browned and caramelized. How long you'll need to grill depends on the thickness of the stems. For thicker ones, it should take about 8 minutes. For thinner ones like the ones shown here, 3-4 minutes are all it takes.
You can top the cooked broccolini with red pepper flakes and/or grated parmesan before serving.
Video
Notes
You don't want your grill too hot because then the broccolini will burn before it has a chance to become tender.
I prefer garlic powder (or garlic granules) to minced fresh garlic in this recipe. The powder better coats the broccolini and doesn't burn as easily as fresh garlic.
How long you'll need to grill depends on the thickness of the stems. For thicker ones, it should take about 8 minutes. For thinner ones, 3-4 minutes are all it takes. The photo below shows the difference in thickness you can expect when shopping for broccolini.
You can keep the leftovers in the fridge, in an airtight container, for 3-4 days. Reheat them in the microwave at 50% power or in a 350°F oven. You can also enjoy them cold, antipasti-style.