In a mixing bowl, combine flour, baking powder, and salt, creating a well in the center. Pour in melted vegan butter and warm dairy-free milk, then mix until a smooth dough forms. Knead for a few minutes until elastic, then wrap the dough in plastic wrap and refrigerate for at least 30 minutes to firm it up for easy handling.

While the dough chills, thaw and drain the frozen spinach thoroughly. In a skillet, heat olive oil over medium heat, and sauté the chopped onion and garlic until soft and fragrant, about 5 minutes. Add the drained spinach, season with pepper, chili, and nutmeg, cooking for another 2-3 minutes before mixing in shredded vegan cheese. Allow the filling to cool completely.

Once your dough has chilled, lightly flour your work surface and roll the dough to about 1/8-inch thickness. Using a 4-inch round cutter, cut out circles of dough. Place about a tablespoon of the cooled spinach filling in the center of each circle, then fold the dough over to create a half-moon shape. Use a fork to crimp the edges securely.

Preheat your oven to 392°F (200°C). On a baking sheet lined with parchment paper, arrange the empanadas and brush them generously with a mixture of olive oil and soy milk for a golden finish. Bake in the preheated oven for 20 minutes or until they turn golden brown and crispy. Once done, remove from the oven and let them cool slightly before serving.