Position racks in the top and bottom thirds of the oven and preheat to 500 degrees . On a large baking sheet, combine the fennel, onion, asparagus, 1 1/2 tablespoons olive oil, 1/2 teaspoon salt and 1/4 teaspoon pepper; spread out evenly on the baking sheet. Roast on the top rack of the oven until tender, 12 to 15 minutes. Transfer to a plate.
Meanwhile, in a small saucepan, heat 2 tablespoons olive oil over low heat; add the garlic and cook until golden, 2 to 3 minutes. Transfer to a food processor along with the beans and bean liquid; puree until smooth. Season with salt and pepper.
Add the remaining 1 1/2 teaspoons olive oil to the baking sheet. Add the dough and, using oiled hands, press and stretch to fill the pan. Bake on the bottom rack for 8 minutes. Quickly spread the bean puree evenly over the dough. Scatter the vegetables on top, season with salt and pepper and bake until the crust is crisp, 8 minutes.