In a small microwave-safe bowl, whisk together the white chocolate chips and 3 tablespoons heavy cream. Heat for 30 seconds and then stir until smooth. Let cool to closer to room temperature before adding to your buttercream.
In the bowl of a stand mixer fitted with a paddle attachment, whip up the butter until it’s light and fluffy. Add in the white chocolate mixture (slightly cooled). Add the remaining ¼ cup heavy cream, vanilla, and salt. Whip up to combine and then scrape down the sides with a spatula.
With the stand mixer on low speed, add the powdered sugar about a half cup at a time. The buttercream will be thick. Add a little more heavy cream to thin it out if needed (1 tablespoon at a time), and then flip the mixer to high speed and beat for 2 minutes to lighten the color and texture of the buttercream.
Transfer 1½ cups buttercream to a separate bowl and stir in the molasses, ginger, cloves, and brown gel coloring. Add to a piping bag without a piping tip.
Transfer 1/4 cup of the white chocolate buttercream to a small bowl, then stir in 1 small drop of green gel coloring. Add this green buttercream to a piping bag with a very small circle piping tip. Set aside.