Preheat your oven to 375°F (190°C) and line a baking sheet with parchment paper.
Begin by making the crust. In a large bowl, mix together almond flour, coconut flour, and salt. Cut in the chilled butter using a pastry cutter or your fingers until the mixture resembles coarse crumbs.
Add the egg to the flour mixture and mix until a dough forms. If the dough is too dry, add ice water, one tablespoon at a time. Wrap the dough in plastic wrap and chill in the refrigerator for 10 minutes.
While the dough is chilling, prepare the filling. Heat olive oil in a pan over medium heat. Sauté the onion and garlic until translucent, about 3 minutes. Add the spinach and cook until wilted. Remove from heat and let cool.
In a mixing bowl, combine the sautéed spinach mixture, crumbled feta, mozzarella, sun-dried tomatoes, black pepper, and nutmeg. Mix until well combined.
Roll out the chilled dough between two sheets of parchment paper into a 12-inch circle. Transfer the dough onto the prepared baking sheet.
Spread the spinach and feta mixture over the center of the dough, leaving about a 2-inch border all around.
Gently fold the edges of the dough over the filling, overlapping slightly, to create a rustic look.
Bake for 25 minutes, or until the crust is golden brown.
Let the galette cool for 5 minutes before slicing and serving.