Beat the softened butter in a stand mixer until creamy, about 1-2 minutes. Add eggs and vanilla extract, and mix until combined. Gradually incorporate the cake mix until a soft dough forms. Add green food coloring to achieve desired shade.

Preheat oven to 350°F (175°C). Line a baking sheet with parchment paper. Scoop tablespoons of dough onto the sheet, spacing cookies 2 inches apart.

Bake cookies for 8-10 minutes or until edges are lightly golden. Cool on wire rack for 5 minutes.

In a bowl, beat softened butter and marshmallow cream until creamy. Gradually add powdered sugar and mix. Stir in milk and mint extract for filling consistency.

Once cooled, pipe mint filling onto half of the cookies and top with the remaining cookies to create sandwiches.