Prepare the filling: Line a small tray with parchment paper or use a silicone mold. Pipe twelve 1-tablespoon portions of Kinder spread or Nutella and freeze until completely firm, at least 30 minutes. Skip this step if making unfilled cookies.
Make the dough: In a large bowl, cream the butter, granulated sugar, and brown sugar until smooth and pale. Add the egg and vanilla and mix until fully incorporated. Add the flour, baking soda, and baking powder and mix just until a cohesive dough forms. Fold in the chopped Kinder chocolate. Cover and refrigerate the dough for 30 minutes to firm.
Portion the dough into twelve equal balls, about 2 ounces/60 grams each. Press a frozen round of filling into the center of each portion and seal the dough completely around it. Arrange on a tray and freeze for 10 minutes.
Heat the oven to 375°F/190°C. Line a baking sheet with parchment paper.
Space the cookies well apart; for thick, uniform cookies, place an 8-centimeter/3-inch ring around each portion. Bake until the edges are set and lightly golden while the centers remain soft, 12 to 13 minutes.
Let cool on the baking sheet until the cookies firm up, then transfer to a rack to cool completely. Finish with melted chocolate and chopped Kinder before serving.