Preheat oven to 350 degrees F. Line standard muffin tins with paper liners. Whisk together flour, baking soda, and salt. In another bowl, whisk sugar, molasses, and eggs until smooth; whisk in melted butter and the hot water. Stir in flour mixture until just incorporated, then stir in ginger.
Divide batter evenly among lined cups, filling each three-quarters full. Bake, rotating tins halfway through, until a cake tester inserted in centers comes out clean, about 20 minutes (cupcakes will not be domed). Transfer tins to wire racks t cool completely before removing cupcakes. Cupcakes can be stored overnight at room temperature, or frozen up to 2 months, in airtight containers.
For the whipped cream, whisk heavy cream until soft peaks form. Add confectioners' sugar, and whisk until combined. If not using immediately, whipped cream can be refrigerated, covered tightly, up to 3 hours in airtight container.
To finish, dollop whipped cream onto cupcakes, and dust lightly with ground ginger. Serve immediately.