Grilled Vegetable Pizzas

Name: Grilled Vegetable Pizzas
Ingredients: 2 tablespoons red-wine vinegar; 1 teaspoon Dijon mustard; 1 ½ teaspoons finely chopped fresh oregano; Kosher salt and freshly ground pepper; ¼ cup extra-virgin olive oil, plus more for brushing; 12 ounces shiitake- or portobello-mushroom caps, or a combination; 2 medium zucchini, sliced lengthwise into ½-inch-thick planks; 1 bunch lacinato kale, thick stems and center ribs removed; 1 medium red onion, peeled and cut into ½-inch-thick rounds; 4 store-bought flatbreads; 12 ounces low-moisture mozzarella; 3 ounces blue cheese, crumbled