Preheat the oven to 350 degrees F. Line a muffin pan with paper liners.
In a small sauce pot, melt butter and molasses and bring to a boil over medium heat. Turn off the heat and pour into a large mixing bowl and let cool for 5 minutes. Mix in the sour cream and orange zest.
While the molasses mixture is cooling, sift the flour, baking soda, ginger, cinnamon, cloves, and salt together into a small bowl. With the mixer running on the lowest speed, add a little of the flour mixture to the molasses mixture at a time, until it is smooth. Turn off the mixer and stir in the crystallized ginger into the mixture with a spatula.
Using a 2-inch scoop, divide the batter among the muffin pan. Place the cupcakes inside the preheated oven and bake on the middle rack until a toothpick comes out clean, about 25 to 30 minutes.
Cool the cupcakes for at least 10 minutes, before removing from the pan.
The Frosting: Using an electric mixer, mix the cream cheese, butter, orange zest and vanilla in a bowl, until just combined. Next, add in the sugar and continue to mix the frosting, until smooth.
When the cupcakes are cool, frost them generously and garnish with minced crystallized ginger.
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