Preheat a gas grill or prepare a fire in a charcoal grill.
In a small bowl, whisk together the vinegar, garlic, oregano, cumin, mustard, pepper flakes, olive oil, and orange juice (reserve the zest for garnish). Set aside.
Cut the eggplant into 1/2-inch-thick slices. Cut the peppers into quarters and remove the cores and seeds. If using baby zucchini, remove the blossoms and set aside; cut the zucchini lengthwise in half. If using small zucchini, cut lengthwise into 1/4-inch-thick slices (discard the first and last slice from each). Cut the onions into 1/4-inch-thick rounds. Trim the scallions. Snap off the tough bottom parts of the asparagus stalks.
Place the vegetables on two large baking sheets. Brush lightly with some of the marinade and season lightly with salt. Place on the grill over medium-high to high heat (you will probably have to cook the vegetables in batches) and cook, turning once or twice, until tender and slightly charred on both sides: the eggplant will take about 8 to 10 minutes, the peppers 10 to 12 minutes, the zucchini 6 to 8 minutes, the onions and scallions 4 to 6 minutes,and the asparagus 5 to 7 minutes. Remove each vegetable from the grill as it is done and return to the baking sheets.
Cut the peppers into 1/2-inch-wide strips. Arrange the vegetables decoratively on a large serving platter and drizzle with the remaining marinade. Sprinkle with the orange zest, the zucchini blossoms if you have them, and the basil. Serve warm or at room temperature.