Toss the asparagus with 2 tablespoons of the olive oil in a medium bowl. Season lightly with salt and set aside.
Place the presoaked beans in a large stockpot and cover with 6 cups fresh water. Season with salt.
Slowly bring to a simmer and cook until the beans are tender, about 40 minutes, adding additional water if necessary. Be careful not to let the beans boil.
Drain the beans, reserving the cooking water. Transfer the beans to the container of an electric blender and cover by 1 inch with the cooking water. Cover and, with the motor running, add the remaining ¼ cup of the olive oil in a steady stream through the opening in the lid. Add additional water, if necessary, to achieve a pancake-batter consistency. This will ensure that as the puree cools, it’s still spreadable.
Spread the bean puree over the unbaked crust. Arrange the asparagus over the puree.
Bake according to the instructions in the dough recipe, using the broiler method to slightly char the asparagus.
Remove from the oven and arrange the ham over the top. Return to the oven for another 2 to 3 minutes to warm the ham.
Grate Parmesan over the top and season with black pepper.