Heat grill to medium. Once it's hot, clean the grill grate with a wire brush.
Toss the broccoli and jalapeños with the oil in a large bowl. Grill, turning occasionally, until tender and lightly charred, about 20 minutes. Cool, then finely chop.
Mash the avocados with the onion, cilantro, lime juice, 1 teaspoon salt, and 1/2 teaspoon pepper in a large bowl. Fold in the chopped broccoli and jalapeños. Serve with the tortilla chips.