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. Brush a rimless baking sheet with olive oil.
Roll and stretch pizza dough to 16x11-inch oval. Transfer to baking sheet. Mix 1 tablespoon 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. Slice the Parmesan over the top, then lightly sprinkle with kosher salt and generously with cracked pepper.
Bake pizza until crust is browned and asparagus is tender, about 15 minutes.
Transfer to cutting board. Sprinkle with remaining green onions and sun-dried tomatoes.
Cut into pieces.