Preheat oven to 500 for at least 20 minutes. Place a baking stone or baking sheet in the oven to preheat.
Combine basil, salt and garlic in a food processor. Turn on to puree. With the machine running, drizzle in the olive oil. You may need to stop and scrape the sides of the workbowl a few times. Set aside.
Lay out a sheet of parchment paper on your work space. Using floured hands, pull and press the pizza dough into your desired shape on the parchment.
Spread the basil mixture over the dough. Top with potato slices, mostly in a single layer, but some can overlap. Layer dollops of goat cheese on top.
Take the baking stone out of the oven. Transfer the pizza, parchment and all, to the stone, and place back in the oven. Cook for 10-15 minutes. The dough should be starting to brown, and potatoes should be cooked through.
To serve, lay the greens atop the pizza and cut into wedges.