Combine butter, sugar, and molasses and use an electric mixer or stand mixer with paddle attachment to beat until ingredients are creamy and well-combined.
Stir in egg and vanilla extract until well-combined. The mixture may look piecey/like it's separating, this is fine and it will come together when you add the dry ingredients.
In a separate, medium-sized bowl, whisk together flour, baking soda, salt, and spices (ginger, cinnamon, cloves, and nutmeg).
With mixer on low speed, gradually add the dry ingredients to the butter mixture until the dough is smooth, cohesive, and completely combined.
Divide the dough into two parts (it will be quite sticky, use a spatula) and wrap each tightly in plastic wrap and refrigerate for at least 3 hours or overnight.
Once dough has chilled, preheat oven to 375F (190C) and line a baking sheet with parchment paper (alternatively bake cookies directly on ungreased baking sheet).
Generously flour a clean surface and lightly flour the dough as well (see note).
Use a rolling pin to roll the dough to be approximately ¼” (.6cm) thick, and use a cookie cutter (my cookie cutter for these was about 3.5” long) to cut out shapes. Use a spatula to place cookies on prepared baking sheet, spacing at least 2" apart and then transfer to 375F (190C) oven, and bake for 8-10 minutes.
Allow cookies to cool completely on baking sheet before decorating.
Combine sugar, 2 Tablespoons of milk, corn syrup, and vanilla extract in a medium-sized bowl and stir until combined. Look for a consistency where the icing that drizzles off the spoon and back into the bowl holds its shape for several seconds before dissolving back into the rest of the icing. If frosting is too thick, add more milk, about a teaspoon at a time, until the frosting is thick but pipeable. If too thin, add additional powdered sugar until desired texture is reached.
Transfer to a piping bag with a piping tip (I used Wilton #5), or place in a Ziploc bag and snip a small piece of the corner off. Pipe frosting on cookies and decorate with decorative candies, if desired.
Allow frosting to harden before enjoying (this took only about 30 minutes for me, but may take longer if your frosting is wetter).
Keep uneaten cookies sealed in an airtight container at room temperature.