Freeze the butter for at least 30 minutes. Wash, peel, and dice fresh peaches into 1/2-inch cubes, then pat dry with paper towels.
Preheat oven to 400°F and line a baking sheet with parchment paper.
In a large bowl, whisk together flour, sugar, baking powder, salt, cinnamon, and nutmeg.
Grate frozen butter into the flour mixture using a box grater. Toss with a fork to coat and keep cold.
Add diced peaches to the flour mixture and toss gently to coat.
In a medium bowl, whisk together heavy cream, sour cream, egg, vanilla, and almond extract until smooth.
Pour wet ingredients into dry and stir with a fork until a shaggy dough forms. Do not overmix.
Turn dough onto a lightly floured surface and gently pat into an 8-inch circle about 1 inch thick. Cut into 8 wedges.
Transfer wedges to baking sheet, brush tops with heavy cream, and sprinkle with coarse sugar if desired.
Bake for 20 to 25 minutes until golden brown. Cool on baking sheet for 5 minutes, then transfer to a wire rack.
Whisk together powdered sugar, heavy cream, vanilla, almond extract, and salt until smooth. Drizzle over warm scones.