Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper.
To make the oat flour, place 1¾ cups old-fashioned oats in a food processor and process until finely ground, about 1 minute. Pour into a bowl and scoop 1¼ cups oat flour back into the processor. Reserve any remaining flour for another use. Add all-purpose flour, sugar, and baking powder to the processor. Pulse briefly to combine.
Add chilled butter to the processor and pulse until the mixture is pale yellow and the consistency of a fine meal. Add the hazelnuts to the processor and pulse to mix. Pour ¾ cup heavy cream (or ½ cup 2 % milk) into the processor and pulse quickly until just mixed.
Turn the mixture out onto a generously floured surface. Sprinkle nectarine pieces over the dough. Lightly dust your hands with flour and gently knead to mix in the nectarine, and make into a ball. Using the palms of your hands, roll the dough into a log shape, about 14 inches long and 1¼ inches high). Using a spatula or scraper, press the dough down lightly on top and against each short end to flatten.
Cut the rectangle in triangles cutting at an angle, for a total of 12 to 14 scones.
Arrange the scones on the prepared baking sheet. Using about 1 tablespoon heavy cream (or 2% milk), lightly brush the tops of the scones. In a small bowl, mix together 1 teaspoon sugar and cinnamon. Lightly sprinkle the cinnamon mixture on top of each scone.
Bake for 15-18 minutes, or until the surface of the scones crack and are golden brown. Cool on the tray or on a cooling rack. Serve.
(Make ahead: The scones can be made ahead and frozen. Place the raw scones on a baking sheet lined with waxed paper. Place in the freezer uncovered. When the scones are completely frozen, place them in plastic freezer bags. Take them out a few at a time and bake for 17-21 minutes at 375 degrees F.)