Preheat oven to 350° and either spray a mini muffin pan with nonstick cooking spray, or line with cupcake liners.
In a medium bowl, whisk flour, baking soda, ginger, cinnamon, and pumpkin pie spice together. Set aside.
In a small saucepan, heat milk and brown sugar together just until sugar is melted and mixture is lukewarm.
In another small saucepan, heat molasses and corn syrup until lukewarm.
While both pans are cooling, cut cold butter into flour mixture using a pastry blender until mixture is crumbly.
Once both pans have cooled a bit, add milk mixture to flour mixture and stir until blended. Then add molasses mixture and stir.
Add egg and whisk until well combined.
Fill each cupcake tin ⅔ full of batter.
Bake in oven for 10 minutes or until toothpick comes out clean.
Remove from oven and let cool completely in pan.
In a medium bowl, beat cream cheese and butter together until creamy.
Add vanilla and cinnamon, mix well.
Gradually add powdered sugar and beat until smooth.
Mix molasses into mixture and blend well.
Once cupcakes have completely cooled, pipe a dollop of frosting onto each one.