Preheat oven to 375 degrees.

Place lemon cake mix into a large bowl and the strawberry cake mix into another large bowl.

Mix 2 eggs, 1/3 cup vegetable oil, and 1 tsp lemon extract into each flavored cake mix until well blended.

Place dough in the refrigerator for 20 minutes to firm slightly.

Take 1 rounded teaspoons of lemon dough and roll into a ball.

Do the same with the strawberry dough.

Combine the lemon and strawberry dough to make one large ball.

Place the dough ball in a bowl with 1 cup of powdered sugar, and roll to lightly coat in powdered sugar.

Place on a parchment covered baking sheet at least 2 inches apart.

Repeat with remaining dough.

Bake 10 minutes until they turn slightly golden and are cooked through.

Transfer to wire rack and let cool completely before frosting and serving.

Whisk together 1 cup powdered sugar with 1 tablespoon of milk until combined.

Add more milk for desired consistency.

Once the cookies reach room temperature, drizzle icing on each cookie with a fork or piping bag.