Oil the grate on your grill, and fire up the grill on high. Close the lid and heat for about 5 minutes, until grate is very hot. Lightly baste the peppers, zucchini, and na'an bread with about 2 tablespoons of the olive oil.
Grilling in batches, arrange the vegetables on the grill over direct heat and grill for 4 - 5 minutes per side. The peppers should be limp, and the zucchini softened. Slice each pepper half in half again, across their lengths. Dice the zucchini into 3/4-inch cubes.
Grill the na'an until slightly crisped, about 3 - 4 minutes per side. Tear into medium-sized shards.
Heat up the remaining tablespoon of olive oil in a small skillet and add the chickpeas, salt, and cumin. Sauté until crispy, about 7 minutes.
Combine the grilled vegetables, bread, chickpeas, and all of the remaining Fattoush ingredients in a large bowl, and lightly toss. Mix the the Buttermilk Dressing (below) just before serving.