Place potatoes in a small pot and cover with salted water. Bring to a boil, and cook 10 minutes. Drain and let cool. Slice potatoes lengthwise into thin strips. Set aside.
In a medium saucepan, warm 2 tablespoons oil over medium heat. Add half the garlic, and cook until fragrant, about 1 minute. Add baby kale, and sauté until just wilted, about 3 minutes.
Heat oven to 500°F. Flour an over turned baking sheet. Stretch pizza dough to a 13-by-9-inch rectangle, and transfer to baking sheet.
Drizzle dough with remaining oil, and sprinkle with remaining garlic. Top with sliced potatoes, green onions, kale, mozzarella, and chèvre. Finish with a dusting of grated Parmigiano Reggiano, salt, and pepper.
Bake 10 to 15 minutes, or until bottom of crust has browned and cheese is bubbling. Transfer to a cutting board and let rest 5 minutes before serving.