Preheat the oven. Preheat the oven to 400°F and line a baking sheet with parchment paper.
Whip the cottage cheese. Add the cottage cheese to a food processor and blend until completely smooth and creamy. Set aside.
Mix the dry ingredients. In a large mixing bowl, whisk together the gluten-free flour, baking powder, and pumpkin pie spice until well combined.
Add the wet ingredients. Add the whipped cottage cheese, pumpkin puree, and coconut sugar to the flour mixture. Stir with a spatula until a shaggy dough begins to form.
Bring the dough together. Use your hands to gently mix and fold the dough until it is almost completely combined.
Add the frozen butter. Using a box grater, grate the frozen butter directly into the dough. Gently fold and knead the dough just until the butter is evenly incorporated and the dough comes together. Avoid overworking it so the dough isn't tough and the butter isn't melted before baking.
Shape the scones. Transfer the dough to a lightly floured surface. Gently shape it into an approximately 8-inch round disc. I like to take the ball of dough and roll it out with a rolling pin lightly until it is about 8 inches wide.
Cut into wedges. Cut the dough into 8 equal wedges with a sharp chefs knife or a bench scraper, and transfer them to the prepared baking sheet, leaving a little space between each scone.
Bake. Bake for 16–20 minutes, or until the scones are set and lightly golden on the edges. Keep an eye on the bottoms toward the end of the baking time so they don't become too dark.
Make the glaze. While the scones bake, whisk together the milk, vanilla, and powdered sugar (or monk fruit) in a small bowl until smooth.
Glaze and serve. Allow the scones to cool slightly for 10-15 minutes before drizzling the glaze over the top. Serve and enjoy!