Preheat the oven to 425 degrees F. Line 2 baking sheets with parchment paper.
Put the asparagus on 1 baking sheet in a single layer and the carrots and onions on the other in a single layer. Spray the vegetables generously with cooking spray and sprinkle with a few pinches of salt. Cook, stirring about halfway through, until tender and slightly caramelized, 15 minutes for the asparagus and 40 minutes for the carrots and onions. Set aside to cool.
Meanwhile, combine the romaine, iceberg lettuce, garbanzo beans, mozzarella, salami and tomatoes in a large bowl.
In a small bowl, whisk together the oil, vinegar, 3/4 teaspoon salt and 1/4 teaspoon pepper until well blended. Set aside.
When cool enough to handle, chop the roasted vegetables into 1/4 inch to 1/2 inch pieces and add to the salad. Add the dressing and toss thoroughly. Add salt and pepper to taste, if necessary.