Finely shred the cabbage into 1/8-inch strips using a sharp knife or mandoline, then shred the carrots using the large holes of a grater. Slice the scallions into thin rounds, separating the white and light green parts from the dark green tops—you'll use them at different times for better flavor. Mince the garlic cloves finely. This prep work ensures everything cooks evenly and prevents any large pieces from breaking your fritters apart.
In a small bowl, combine the flour, salt, pepper, paprika, coriander, and cayenne pepper. In a large mixing bowl, crack the eggs and beat them lightly. Add the shredded cabbage, grated carrots, minced garlic, and the white and light green parts of the scallions to the eggs, then sprinkle the dry ingredient mixture over top. Fold everything together gently until the vegetables are evenly coated and the mixture holds together when squeezed. I like to let this sit for 2-3 minutes while I heat the fat—the vegetables release a bit of moisture that helps bind everything together.
Place a large skillet over medium-low heat and add the butter (or fat of your choice). Let it melt slowly for about 1 minute, then increase the heat to medium. You want the fat hot enough that the fritters sizzle immediately when they hit the pan—this creates a golden crust—but not so hot that they brown before the inside cooks through. The butter should be foaming gently when you're ready to cook.
Using a sturdy spoon or ice cream scoop, portion the batter into roughly 2-inch balls and carefully place them in the hot fat, spacing them about 2 inches apart. Using the back of the spoon, gently flatten each ball into a patty about 1/2-inch thick. Fry for 3 minutes on the first side without moving them—they need time to develop that golden-brown crust. Flip carefully and fry another 3 minutes on the second side until both sides are deep golden brown and crispy. I find that resisting the urge to flip too early is key to getting truly crispy fritters.
Transfer the finished fritters to a paper towel-lined plate to drain any excess fat. While they're still warm, sprinkle them lightly with a pinch of salt and garnish with the reserved dark green scallion tops for a fresh, bright flavor contrast. Serve the fritters warm for the best texture, though they're also delicious at room temperature.