In a large bowl, combine the shredded cabbage, grated carrots, and chopped green onions. Mix well.
Add the flour, Parmesan cheese, egg, garlic powder, onion powder, salt, black pepper, and paprika to the vegetable mixture. Stir until everything is well combined.
Heat the vegetable oil in a large skillet over medium heat.
Using a spoon, drop heaping tablespoons of the cabbage mixture into the hot oil, flattening them slightly with the back of the spoon. Fry in batches, making sure not to overcrowd the pan. Cook for about 3-4 minutes on each side, or until golden brown and crispy.
Remove the fritters from the skillet and place them on a paper towel-lined plate to drain excess oil.
For the garlicky dip, mix together the Greek yogurt, mayonnaise, minced garlic, lemon juice, salt, and pepper in a small bowl until smooth.
Serve the crispy cabbage fritters warm with the garlicky dip on the side.