Preheat your oven to 350°F and line two baking sheets with parchment or silicone mats. Cream the butter and powdered sugar until light and fluffy. Add the egg, vanilla, and almond extract and mix until combined. Stir in flour and dry pudding mix until just blended, then fold in mini chocolate chips.
Scoop tablespoon-sized portions of dough, roll them into balls, and coat each in finely chopped pecans. Place on prepared baking sheets about 2 inches apart. Press a small indentation into the center of each dough ball using the back of a teaspoon.
Bake for 10–12 minutes or until edges are lightly golden. If the centers puff up during baking, gently re-press them while still warm. Let cookies cool completely on a wire rack.
In a separate bowl, cream the butter, powdered sugar, vanilla, and milk until smooth. Spoon or pipe the frosting into the cooled cookie centers. Optionally, drizzle with melted chocolate for an extra touch.