Preheat the oven to 375˚ F. Line 2 baking sheets with parchment paper. Whisk the flour, cocoa powder, baking soda and salt in a medium bowl. In a separate bowl, beat the butter and brown sugar with a mixer on medium-high speed until pale and fluffy, 3 to 5 minutes. Beat in the egg and vanilla. Beat in the flour mixture on low speed. Stir in the white chocolate chips and chopped peach.
Arrange 24 balls of dough, about 2 heaping tablespoons each, about 2 inches apart on the baking sheets.
Bake until set around the edges, 12 to 15 minutes. Let cool 10 minutes on the pans, then transfer to a rack to cool completely.