Preheat the oven to 400 degrees F (200 degrees C). Line a baking sheet with parchment paper.

Place cauliflower into a food processor; blend until finely ground.

Cook cauliflower, water, and salt in a large skillet over medium-high heat until fragrant and most of the water is evaporated, 5 to 6 minutes. Cool completely.

Transfer cauliflower to the center of a clean dish towel. Wrap and squeeze tightly to remove excess moisture. You should have about 1 1/2 cups cauliflower pulp.

Stir together cauliflower pulp, egg, goat cheese, Parmigiano-Reggiano cheese, and cayenne pepper in a large bowl to form a soft dough. Gather into a ball and place in the center of the prepared baking sheet. Press dough into a circle, about 1/4-inch thick.

Bake in the preheated oven until golden brown, about 40 minutes. Cool and turn crust over before topping.