Preheat oven to 450°F (232°C) with the rack on the middle shelf.
Add the flour, sugar, baking powder, cinnamon, and salt to a food processor. Pulse a few times to mix.
Scatter the cold butter across the flour. Pulse until it resembles cornmeal or wet sand, approximately 10-12 pulses.
Pour out the flour mixture into a bowl. Add the chopped peaches and heavy cream. Mix until just barely incorporated. Do not overmix (a little dry mixture is okay and preferred to overmixing).
Dump the dough out onto a lightly floured surface. Gently and briefly knead or press to incorporate the dough and press into a 1½-2 inch slab. Kneading should be just 30-45 seconds and the dough will be sticky.
Flour a round cookie cutter and cut out scones by pressing straight down (do not twist). Repeat with remaining dough, very gently pressing back together. (Re-pressed dough will likely result in scones slightly more dense or flat due to the extra handling).
Place the scones on a lined baking sheet. If desired, sprinkle with additional sugar for texture and color.
Chill the scones in the refrigerator for 30 minutes. This is not mandatory, but will help the scones rise and be light.
Bake for 13-15 minutes until lightly golden brown. Rotate the baking sheet halfway through baking. Cool on a wire rack for at least 10 minutes. Store in a sealed container for up to 5 days.
If preferred, make 8 triangle scones instead by following the instructions for our Coconut Oatmeal Raisin Scones at step 7.Scones can be covered and refrigerated up to 24 hours before baking after cutting.Freeze the scones after cut and before baking for up to a month. Then bake as desired and directed in instructions, without thawing, although you may need to bake them a few minutes longer.