Cut the leaves off the kohlrabi and peel the bulb. Chiffonade a few leaves and set aside. Peel 1 carrot. Shred the vegetables in a food processor, or by hand using a grater. Squeeze the shredded vegetables in a tea or cheese cloth (or with your hands) to remove moisture, then add to a medium bowl with 1 egg, ¼ teaspoon kosher salt, and ¼ teaspoon cayenne. Mix to combine.
Place ½ cup oil in a large skillet (enough for ¼-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.
In a small bowl, mix ½ avocado, ¼ cup plain yogurt, juice from ½ lemon, and ¼ teaspoon kosher salt to make the avocado cream (or blend the ingredients together in a food processor).
Serve fritters with avocado cream and garnish with the chiffonaded kohlrabi leaves.