Preheat a grill or grill pan over medium-high. Brush the zucchini with oil, season with salt and pepper, and grill until crisp-tender and charred in spots, 2 to 3 minutes per side. Cut into 1/4-inch cubes and transfer to a large bowl. Toss with the beans, peppers, corn, onion, quinoa and cilantro.
In a small bowl, whisk the vinegar, lime juice, garlic and cumin. Gradually whisk in 1/4 cup oil; season. Pour over the vegetables and toss to coat; season the salad.
Divide the radicchio leaves and avocados among 4 plates and top with the salad.