Heat olive oil and butter in a skillet over medium heat. Stir in garlic and ginger; cook and stir until fragrant, about 3 minutes. Stir in kohlrabi, and season with salt and pepper. Cook and stir until kohrabi has softened, 3 to 4 minutes. Toss in yellow squash and continue to cook until squash is tender for 4 more minutes. Stir in the green onion, spinach, and nutmeg. Add more salt and pepper, as needed. Cook until the spinach has wilted, about 1 minutes. Set mixture aside to cool.
Preheat an oven to 425 degrees F (220 degrees C). Line a baking sheet with parchment paper. Beat the egg with water in a small bowl; set aside.
Roll out the pie crust by running a rolling pin over it once or twice. Cut out about 16 6-inch circles using a large cookie cutter or cereal bowl. Fill the center of each circle with about 1 tablespoon of the kohlrabi mixture. Brush the edges of the pastry with water, then fold the dough in half. Crimp the edge of the dough with a fork to seal, and place on the prepared baking sheet. Repeat with the remaining pastry and vegetable filling. Prick each empanada with a fork, then brush with the egg wash.
Bake in the preheated oven until golden brown and flaky, 5 to 7 minutes. Serve hot from the oven.
