3 tbsp olive oil (2 for brushing on the dough, 1 for tossing the asparagus)
Place potatoes in small saucepan. Add enough water to cover by 1 inch. Sprinkle with salt. Bring to boil and cook until potatoes are tender, about 10 minutes. Drain. Cool. Cut potatoes into thin slices.
Preheat oven to 450°F. On a rimless baking sheet, roll and/or stretch pizza dough to 16×11-inch oval. Mix 2 tablespoons olive oil and garlic in small bowl. Brush garlic oil over dough. Sprinkle 3/4 of green onions over, then mozzarella, leaving 1/2-inch plain border. Top with potato slices and goat cheese. Toss asparagus and 1 tablespoon oil in medium bowl. Scatter asparagus over pizza. Sprinkle with Parmesan, then with salt and generously with pepper.
Bake pizza until crust is browned and asparagus is tender, about 18 minutes. Sprinkle with remaining green onions. Cut into pieces.