Preheat the oven to 350°, and line two baking sheets with parchment paper.
In a large bowl, stir together the melted butter and sugar until a coarse mixture forms. Add in the yogurt and vanilla, stirring well. Mix in the peaches. Lightly spoon the flour into the measuring cups, and mix in along with the baking soda and salt, stirring just until incorporated.
Drop tablespoons of dough onto the prepared baking sheets, and bake at 350° for 8-10 minutes, or until just barely set. Cool on the pans for 5 minutes before turning out onto a wire rack to cool completely.