Preheat the oven to 400 degrees F. Line a sheet pan with parchment paper.
In a large bowl, stir the chickpeas, red onions, 2 minced garlic cloves, parsley, cumin, cayenne pepper, 1/2 teaspoon kosher salt, black pepper and flour. Smash the chickpea mixture with a fork.
Stir in the feta and egg until everything is well combined.
Shape the chickpea mixture into 12 balls, about a scant 1/4 cup (not packed). Press them down gently with the palm of your hand or the bottom of a jar.
Bake the fritters for 25-30 minutes until they are golden brown on both sides, flipping them over halfway through baking.
While the fritters are in the oven, make the sauce, stir the tahini, 1 minced garlic clove, lemon juice, pinch of salt and water in a small bowl. (The sauce should be a thick but pourable consistency. If needed, you can add more water 1 teaspoon at a time, stirring after each addition to thin it out.)
Serve warm with the sauce on the side or drizzled on top. Sprinkle the fritters with chopped parsley.