Whisk the flour, baking soda, ginger, cinnamon, cloves, nutmeg, and salt together in a medium bowl until combined. Set aside.
In a large bowl or stand mixer fitted with a paddle attachment, beat the butter and both sugars together on high speed until creamy and combined, about 2 minutes. Add the molasses and mix until combined. Add the egg and vanilla extract and mix until combined, about 1 minute, scraping down the sides and bottom of the bowl as needed.
With the mixer on low speed, slowly mix the dry ingredients into the wet ingredients until combined. The cookie dough will be slightly sticky. Cover bowl with plastic wrap and chill for 1 hour.
Preheat oven to 350°F. Line a baking sheet with parchment paper or spray with cooking spray and set aside.
Remove cookie dough from the refrigerator. Use a medium cookie scoop or tablespoon to scoop dough and roll into balls. Place 1/3 cup sugar in a shallow dish, and roll each ball in the sugar to coat. Place balls on prepared baking sheet 2 inches apart and bake for 11-12 minutes or until edges appear set and tops appear slightly cracked. Repeat in additional batches if needed.
Remove from the oven and allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.
Meanwhile, place the white chocolate chips and shortening in a microwave-safe bowl, and heat for 30 seconds. Stir, and heat in 15 second intervals until mostly melted. Stir until smooth, then add the molasses and stir until well combined.
Place a sheet of wax paper on a cookie sheet or cutting board. Take the cooled cookies and either dip half into the frosting and place on wax paper, or use a spoon to drizzle frosting on the top, or scoop a spoonful of frosting onto the cookies and spread around. Top with sprinkles of choice and allow frosting to set (it will harden so it won't be messy!)
Once set, they are ready to serve, or you can store in an airtight containter until ready to serve, up to one week.