Preheat your oven to 425°F. Line a large baking sheet with parchment paper.
In a food processor, pulse the cauliflower and garlic until finely chopped. Transfer the mixture to a microwave-safe bowl and microwave on high for 3 minutes. Let it cool slightly.
Stir in the eggs, mozzarella, shredded carrot, 2 tablespoons of chives, and salt. Spread this mixture into a 12-inch circle (about 1/4 inch thick) on your prepared baking sheet.
Bake the crust for 35-40 minutes, or until the edges are browned and crispy.
While the crust bakes, combine the shredded chicken with 1 tablespoon of hot sauce, vinegar, and cayenne pepper in a bowl.
Remove the crust from the oven and top with the chicken mixture and blue cheese. Bake for an additional 5 minutes until the chicken is warmed through and the cheese starts to melt.
Once baked, garnish with celery, the remaining chives, and an extra drizzle of hot sauce. Slice and serve immediately.