Preheat the oven to 400°F. Line a baking sheet with parchment paper and set aside.

Grate the cold butter onto a plate, then transfer it to the freezer while you prepare the remaining ingredients.

Add the cottage cheese, pumpkin puree, maple syrup, and brown sugar to a blender. Blend until smooth, then refrigerate until ready to use.

In a large bowl, whisk together the flour, baking powder, pumpkin pie spice, cinnamon, and salt.

Add the grated butter to the dry ingredients and toss until coated in flour. Use your fingers to work the butter into the dry ingredients until pea-sized pieces form. Be careful not to overmix.

Pour the chilled pumpkin mixture over the dry ingredients. Stir with a rubber spatula or wooden spoon just until a shaggy dough forms. Do not overmix.

Lightly flour a clean work surface. Transfer the dough to the surface and gently form it into a disk. The dough may be slightly sticky or crackly. Do not knead it.

Shape the dough into a 6-inch circle, then cut it into 6 wedges. Gently reshape the wedges with your hands if needed.

Arrange the scones on the prepared baking sheet at least 2 inches apart.

Brush the tops with the beaten egg and sprinkle with turbinado sugar.

Bake for about 20 minutes, or until the tops are lightly golden.

Meanwhile, prepare your glaze of choice. For Glaze Option 1, add all of the ingredients to a blender and blend until smooth. For Glaze Option 2, whisk all of the ingredients together in a small bowl until smooth.

Let the scones cool for 15 minutes, then drizzle with your desired glaze and serve.