Combine crumbs, 1/4 cup ginger, and melted butter. Pat crumb mixture evenly over bottom of a removable-rim 8-inch cheesecake or cake pan (at least 1 3/4 in. deep).
Bake in a 350° oven until crust is slightly browner, 10 to 12 minutes.
Meanwhile, in a blender or food processor, whirl ricotta cheese, egg whites, and lemon juice until very smooth.
In a bowl, mix yogurt cheese, sugar, lemon peel, and vanilla. Add ricotta mixture and stir until well blended (the mixture is thin). Pour into hot or cool crust.
Bake in a 350° oven until center barely jiggles when cake is gently shaken, 50 to 55 minutes. Run a thin-bladed knife between cake and pan rim. Refrigerate cake, uncovered, until cool, at least 2 1/2 hours. (If making ahead, wrap airtight when cool and chill up to 2 days.)
Remove pan rim. Peel kiwi fruit and slice crosswise. Arrange fruit in a ring in overlapping slices on cake; sprinkle with remaining ginger. Cut cake into wedges.