Preheat oven to 350 degrees. Line a standard muffin tin with paper liners. Sift together flours, ground ginger, baking powder, baking soda, and salt; set aside.
With a mixer, cream butter and granulated sugar until pale, about 4 minutes. Beat in eggs one at a time until incorporated. Beat in flour mixture in three batches, alternating with milk, and beginning and ending with flour. Stir in candied ginger until distributed.
Divide batter among liners, filling halfway. Bake until golden and set, about 20 minutes. Transfer tin to rack to cool for 15 minutes. Remove from tin; let cool. Store in an airtight container up to 2 days.
Make glaze a few hours before serving (if glazed cupcakes sit out too long, they will wrinkle). Whisk milk and confectioners' sugar until smooth. Add rose water. Add a small drop of food coloring for pale pink, and stir. Immediately pour glaze on cupcakes (about 1 tablespoon each) just until flush with top of liner. Let set before decorating with sugared rose petals.
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