While it’s easy to grill the larger florets directly on the grates, a grill basket is a great way to capture and caramelize any small crumbles that break loose during slicing.
- Prepare a charcoal grill for two-zone cooking and build a medium-hot fire. If you’re using a grill pan, allow it to heat for 10 minutes before cooking.
- Use a paring knife to core cauliflower and broccoli and cut them into large pieces, reserving any small crumbles. Place vegetables in a large mixing bowl, drizzle with enough olive oil to lightly coat, generously season with salt and pepper, and toss to combine.
- Make the herb oil: Char the chile peppers and garlic cloves in a grill basket (or small cast-iron skillet placed directly on grates), cooking over direct heat and turning as needed until peppers are blackened and mostly tender. Set aside to cool. Stem and seed chiles and lightly chop. Peel garlic. Combine chiles, garlic, cilantro, parsley, vinegar, and a pinch of salt in a blender. With blender running, add olive oil in a slow, steady stream until mixture is very smooth. Add 1 to 2 tablespoons of additional oil or water for desired texture. Add additional salt, vinegar, and pepper to taste.
- Grill cauliflower and broccoli over direct heat until lightly charred on all sides, and then use tongs to move florets to indirect heat and close grill. Cook, flipping every 4 to 5 minutes, until the vegetables are just tender when pierced with a sharp knife. Serve the vegetables warm or at room temperature atop a pool of the spicy oil, or toss them with the oil.