Preheat the oven to 475 degrees F. Put the bread on a baking sheet lined with parchment paper.
Bring a medium pot of water to a boil. Add the asparagus and boil until just barely crisp tender, about 1 minute. Drain and run under cold water to stop the cooking.
Heat the oil in a small skillet or saucepan over medium heat. Add the garlic and red pepper flakes and cook, stirring, until the garlic is golden, 2 to 3 minutes. Brush about half the oil all over the top of the breads. Arrange the zucchini ribbons and asparagus on top and brush lightly with the remaining oil. Sprinkle with salt and top with the Parmesan.
Bake until the bread is crisp and the zucchini is lightly charred in spots, about 12 minutes. Cut into pieces and serve warm or room temperature.