Preheat the oven to 350°F (175°C) and line baking sheets with parchment paper.
In a large bowl, cream together the 1 cup plus 2 tablespoons peanut butter and 1/2 cup softened butter until smooth.
Add 1/4 cup white sugar and 3/4 cup packed brown sugar to the creamed mixture and beat until well blended.
Beat in the egg, 2 tablespoons milk, and 1 teaspoon vanilla until evenly incorporated.
In a separate bowl, whisk together 1 1/3 cups all-purpose flour, 3/4 teaspoon baking powder, and 1/4 teaspoon salt.
Gently add the dry ingredients to the creamed mixture and mix until just almost combined, then fold in 1/2 cup peanut butter chips and 1/2 cup chocolate chips.
Chill the dough for at least 15 minutes to firm up.
Scoop tablespoonfuls of dough and roll into balls, then roll each ball in the 3/4 cup sugar to coat.
Place the coated dough balls on the prepared baking sheets, leaving space between cookies.
Bake for 8 to 10 minutes, or until the edges are lightly browned.
Allow cookies to cool on the baking sheets for 5–10 minutes until firm enough to transfer, then move to a wire rack to cool completely.
If needed, chill the dough between batches.