Beat butter and brown sugar with a mixer on medium until pale and fluffy, about 3 minutes.

Mix in molasses, egg, and sourdough discard until combined.

Whisk flour, baking soda, spices, and salt together, then add to wet mixture in two additions, mixing just until no streaks remain.

Divide dough in half, flatten into discs, wrap, and chill at least 30 minutes.

Heat oven to 350°F. Roll dough between parchment to 1/4-inch thick. Cut with floured cutters, transfer to parchment-lined sheets, and bake 8–10 minutes until edges are set. Cool on sheets 5 minutes, then move to a wire rack. Serve once cooled.