Preheat a grill to medium-high. In a bowl, combine 1/3 cup mayonnaise, 2 tablespoons chopped cilantro, 4 teaspoons fresh lime juice and 1/2 teaspoon chili powder. Cut one 2-pound cauliflower into sixteen 2-inch pieces. In a large bowl, toss the cauliflower with 1/4 cup extra-virgin olive oil and 1/2 teaspoon each chili powder and salt. Thread 4 florets onto each of four 10-inch skewers. Grill, turning occasionally, until browned and crisp-tender, about 10 minutes. Brush with the mayonnaise mixture and sprinkle with 1/3 cup finely grated pecorino-romano cheese and 1 tablespoon chopped cilantro.