Whisk oat flour, baking powder, cinnamon, and salt together in a large bowl. Refrigerate the flour mixture while you complete the next step.
Using a box grater, grate frozen butter. Using a pastry cutter or your hands, combine butter with flour mixture. Return to the refrigerator while you mix the wet ingredients.
Whisk milk, egg, and vanilla together in another bowl. Add wet ingredients to dry ingredients, mix until combined. Then, add in the blueberries. Return dough to refrigerator for at least 10 minutes. (This allows the oats to absorb liquid as needed.)
The dough will be sticky, but you should be able to pull it out of the bowl. If it's too sticky, add more oat flour. If it seems too dry, add 1-2 more tablespoons of milk. (It's more likely to be too sticky.) Place dough on a floured surface (use oat flour) and press into an 8-inch disc (I used the back of a pie pan to measure). Cut into eight wedges.
Place scones on a baking sheet lined with parchment paper or a silicone mat. Do NOT spray the bottom with cooking spray. Brush the scones with milk and sprinkle with sugar. Move scones back to the refrigerator (final time, I promise) for at least 20 minutes. If your fridge doesn't have room for a baking sheet, you can temporarily place scones on a large plate—Preheat the oven to 400F.
Arrange scones 2-3 inches apart on the prepared baking sheet. Bake for 20-22 minutes or until golden brown around the edges and an inserted toothpick comes out clean. Remove from the oven and let cool at least 10 minutes before adding vanilla icing.