Preheat the oven to 375°F. Lightly grease a baking sheet.
In a small bowl, combine the chopped peaches and the fresh thyme leaves. Stir lightly and set aside.
In a large bowl, mix together the white and whole wheat flours, sugar, baking powder, salt, nutmeg and black pepper. Add in the butter, using a fork or a pastry blender.
In a separate bowl, whisk together the eggs, yogurt or sour cream, and the extracts. Stir the wet ingredients into the dry ingredients. Add the peaches, stirring just until everything is combined. The dough will be wet and sticky.
Drop the dough by the 1/4-cupful onto the sheet pan. Using a muffin scoop is really helpful here. Sprinkle the scones with coarse sugar, if desired.
Bake the scones for 20 to 25 minutes, until they're a light golden brown. Remove them from the oven, and let them cool on the pan for a few minutes before transferring to a rack to cool completely.
Serve warm, or at room temperature. Store at room temperature, in an airtight container for several days.