Make the streusel topping: Combine brown sugar, flour, cinnamon, and cold butter. Cut into crumbs and chill until ready to use.
3 Cream butter and sugars until fluffy, about 2 minutes.
4 Add egg and vanilla, mixing until smooth.
5 Stir in flour, baking soda, salt, and cinnamon until dough forms.
6 Fold in diced peaches gently to avoid overmixing.
7 Scoop cookie dough (about 1½ tbsp per cookie) onto prepared trays.
8 Top each with streusel and lightly press down.
9 Bake for 12–14 minutes, or until edges are golden and centers just set.
10 Cool for 5 minutes on the tray, then transfer to a wire rack.