Preheat oven to 350°F (175°C). Line a baking sheet with parchment paper.

In a medium bowl, whisk together flour, baking soda, ginger, cinnamon, cloves, and salt.

In a large bowl, cream the softened butter with brown sugar until light and fluffy.

Beat in the egg, then add molasses and vanilla extract, mixing well.

Gradually add the dry ingredients to the wet ingredients, stirring until combined.

Roll the dough into 1-inch balls and place them on the prepared baking sheet, spacing them about 2 inches apart.

Flatten each ball slightly with the palm of your hand.

Bake for 8-10 minutes, or until the edges are firm but the centers remain soft.

Remove from the oven and let cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.

Meanwhile, prepare the frosting by beating softened butter until smooth, then gradually add powdered sugar, milk, and vanilla extract until creamy and spreadable.

Once the gingerbread cookies have cooled, spread a generous layer of frosting over each cookie.