In a large nonstick skillet, heat Olive Oil (1 tablespoon). Sauté the Parsnip (4) noodles over medium-high heat until soft, about 5 minutes. Season lightly with Sea Salt (to taste) and transfer to a mixing bowl.
Allow to cool for 2 minutes, then stir in Large Egg (4).
Wipe out the skillet, and heat Olive Oil (1 tablespoon) over a medium flame. Fill four ramekins halfway with the parsnip mixture and press down with the back of your spoon to compress the noodles.
When the oil shimmers, add the parsnip buns by inverting the ramekins over the pan and tapping the bottom. Use a spatula to push in any stray noodles and form a round. Cook for 2 to 3 minutes, until nicely browned.
Carefully flip and cook for 2 more minutes on the second side. Remove to a plate and repeat with the remaining parsnip batter in two additional batches. You’ll have 12 total buns.
In a medium mixing bowl, with clean hands, combine the Ground Turkey (1 pound), Fresh Ginger (1 tablespoon), Garlic (2 clove), Cayenne Pepper (1/4 teaspoon), and Sea Salt (to taste). Form the meat mixture into 6 equal balls.
Add Olive Oil (1 tablespoon) to the same skillet you used for the buns and set it over medium-high heat. Add the burgers, 3 at a time, and press down with a spatula to form a thin patty, roughly the same size as the buns.
Cook for 10 minutes, or until the burgers are browned on both sides and cooked through. Repeat with the remaining patties.
To assemble, top the parsnip buns with one turkey burger, a dollop of condiment of your choice, Arugula (to taste), and the second bun.