Prep. Preheat oven to 375°F. Line baking sheets with parchment paper.
Dry Ingredients Whisk together flour, cinnamon, cloves, ginger, baking soda, and salt in a large bowl. Set aside.
Cream butter, shortening, and sugar. Cream butter, shortening, 1/2 cup granulated sugar, and brown sugar in mixer bowl on medium-high until light and fluffy, about 3 minutes.
Add egg and vanilla. Add egg and vanilla, mix on low then medium until combined. Add molasses and mix until incorporated.
Add dry ingredients. Add dry ingredients and mix on low just until no flour streaks remain. Don't overmix.
Shape and roll. Form dough into 1 1/2 inch balls, roll in remaining sugar, place 2 inches apart on baking sheets.
Bake Bake 10 minutes. Let cookies set on baking sheet 4-5 minutes, then transfer to cooling rack.
Make frosting. Beat butter until light, 2-3 minutes. Add powdered sugar, mix until combined. Add vanilla and 3 tablespoons cream, beat until smooth. Add remaining cream if needed.
Assemble. Once cookies are cool, spread 2 tablespoons frosting on flat side of 12 cookies. Top with remaining cookies, pressing gently.