For the cupcakes: Position an oven rack in the center of the oven, and preheat to 350 degrees F. Line a 12-cup muffin tin with paper liners, and coat the liners and the top of the tin with cooking spray.
Whisk the flour, baking powder, cinnamon, clove and salt together in a medium bowl. Beat the sugar and eggs in another medium bowl with an electric mixer on medium-high speed until light and creamy, about 2 minutes. While continuing to beat, gradually pour in the butter, then beat in the orange zest. Adjust the speed to medium-low, and add half the flour mixture. Add the milk, then the remaining flour mixture, taking care not to overmix the batter. It will be thin, like pancake batter; transfer it to a liquid measuring cup to make filling the muffin cups easier.
Divide the batter evenly among the cups of the prepared muffin tin. Bake until the tops spring back when pressed, 20 to 22 minutes. Cool the cupcakes in the tin for a few minutes, then transfer to a rack to cool completely. (The cupcakes can be baked a day ahead and stored in an airtight container at room temperature.)
For the frosting: Bring the cranberries, granulated sugar, orange juice and ginger to a simmer in a small saucepan over medium heat. Cook, stirring frequently, until the sugar dissolves, the cranberries burst and the mixture thickens, about 10 minutes. Let cool completely. Set aside 1/3 cup for garnish.
Beat the cream cheese and butter in a large bowl with an electric mixer on medium-high speed until smooth. Beat in the confectioners' sugar. Add the cooled cranberry mixture, and beat until completely incorporated.
Divide the frosting evenly among the cupcakes, and use a small offset spatula or the back of a spoon to swirl. Garnish each with a dollop of reserved cranberry sauce and a piece of orange zest.
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