Cut the leaves off the kohlrabi and peel the bulb. Peel 1 carrot. Shred the vegetables in a food processor, or by hand using a grater. Squeeze the shredded vegetables in a tea cloth (or with your hands) to remove moisture, then add to a medium bowl with the egg, salt, and cayenne. Mix to combine.
Place the oil in a large skillet (enough for 1/4-inch depth). Heat the oil over medium high heat, then place small patties of the fritter mixture into the oil. Fry on one side until browned, then fry on the other side. Remove and place on a plate lined with a paper towel to drain excess oil.
For the dipping sauce: Remove avocado pit and scoop out the flesh with a spoon. In a small bowl, mix the avocado, plain yogurt, lemon juice, and salt to make the avocado cream (or blend the ingredients together in a food processor).
To serve, slice the green onion. Serve fritters with avocado cream and green onions. Note: These fritters are best eaten warm the day of making; they don’t save well. Like anything made with avocado, the avocado cream sauce will become brown after exposure to air. Make sure to cover the surface with plastic wrap when storing.