Preheat oven to 350°F with rack in middle. Line bottom and sides of a buttered 15- by 10-inch shallow baking pan (1 inch deep) with a sheet of parchment paper and butter parchment.
Melt butter with treacle, sugar, and water in a small saucepan over medium heat, stirring, then cool to room temperature, stirring occasionally.
Whisk together flour, baking powder, and ground ginger in a large bowl.
Whisk in butter mixture and egg yolk until smooth.
Beat egg white in a medium bowl with an electric mixer until it just holds stiff peaks, then fold into batter gently but thoroughly.
Pour into baking pan, spreading evenly, and bake until top is golden and firm to the touch, 18 to 22 minutes. Cool cake in pan 5 minutes, then cover cake with a slightly damp kitchen towel and cool completely, about 1 hour.
Dust cake generously with confectioners sugar, then cover with a sheet of parchment, then with a baking sheet or rack. Invert cake and peel off parchment now on top.
Beat cream until it just holds stiff peaks, then spread evenly over top of cake, leaving a 1/2-inch border.
Sprinkle crystallized ginger over cream.
Roll up cake, starting from a short side, to make a 10-inch log, removing parchment as you go.
If desired, slices of roulade can be frozen (up to 1 week), then lightly sprinkled with turbinado sugar (such as Sugar in the Raw) and broiled (do not thaw first) in a shallow baking pan 5 to 6 inches from heat until golden, about 3 minutes.
Roulade can be made 1 day ahead and chilled, covered.
