Chef John's Cauliflower Pizza Crust

1 head cauliflower, cored and separated into florets
1/2 cup water
1/2 teaspoon salt
2 ounces fresh goat cheese
1/2 ounce finely grated Parmigiano-Reggiano cheese
1 large egg
1 pinch cayenne pepper, or to taste

Preheat oven to 400 degrees F (200 degrees C). Line a baking sheet with parchment paper.
Puree cauliflower in a food processor until finely ground.
Cook ground cauliflower, water, and salt together in a skillet over medium-high heat until fragrant and most of the water evaporates, 5 to 6 minutes. Cool completely.
Transfer cauliflower to the center of a clean dish towel. Wrap and squeeze tightly to remove all excess moisture. You should have about 1 1/2 cups cauliflower pulp.
Stir cauliflower, goat cheese, Parmigiano-Reggiano cheese, egg, and cayenne pepper together in a bowl to form a soft dough. Gather dough into a ball and place in the center of the prepared baking sheet. Press dough into circle about 1/4-inch thick.
Bake in the preheated oven until golden brown and set, about 40 minutes. Cool and turn crust over before topping.