In a large skillet, heat one tablespoon of the olive oil over medium heat. Add the chopped shallot and garlic and sauté for 3 to 5 minutes, or until the shallot is tender.
While the shallot is cooking, scrub and trim the turnip. Run it through a spiralizer to make thin turnip noodles.
Add the turnip noodles and the other tablespoon of olive oil to the skillet. Cook, stirring occasionally, for 5 to 7 minutes or until the turnip noodles are tender.
Use your spoon to create two "nests" for the eggs in the skillet. Crack an egg into the middle of each nest. Turn your oven broiler to high, remove the skillet from the stovetop, and put the entire skillet under the broiler for 3 to 5 minutes, or until the eggs have cooked to your liking. Be careful not to overcook the eggs, and remember to use an oven mitt when transferring the skillet to and from the oven.
Remove the skillet from the oven and transfer the turnip noodles and eggs to a plate. Top with fresh chives, salt, and pepper to taste. Enjoy!