Position a rack in the center of the oven and heat the oven to 350°F. Line three miniature muffin pans (with 12 cups each) with miniature paper cupcake liners.
Sift the cake flour with the ground ginger, nutmeg, salt, baking soda, and baking powder. Whisk to ensure thorough mixing. Using a stand mixer fitted with the paddle attachment (or a hand mixer), beat the butter in a medium bowl on medium speed until smooth, about 1 min. Add 3 Tbs. of the sugar, the vanilla, grated ginger and lemon zest; beat on medium speed for 1 min. Add the remaining sugar, about 2 Tbs. at a time, beating for a few seconds after each addition. Scrape the bowl and beat for another 2 min. Scrape the bowl again. Add the egg and beat on medium-high until very smooth, about 1 min.
Add about one-third of the flour mixture and stir gently with a rubber spatula only until incorporated. Add half the sour cream and stir until incorporated. Repeat with half the remaining flour mixture, the rest of the sour cream, and ending with the last of the flour mixture. Stir in the crystallized ginger.
Divide the batter evenly among the prepared muffin cups, filling each cup about three-quarters full. (Use two regular teaspoons: one to pick up the batter, one to push it off.) Don't smooth the batter.
Arrange the pans in the oven so that there's a bit of space between them and bake until the cupcakes are pale golden and spring back when gently pressed in the center, 17 to 20 minutes. Let the cupcakes cool in the tins on wire racks for 5 minutes and then invert the pans onto the racks to remove the cupcakes. Immediately turn the cupcakes right side up on the racks and let cool completely.
Spoon a heaping teaspoonful of frosting onto the center of each cupcake and spread and swirl it with the back of the teaspoon. If you like, garnish with sliced crystallized ginger or strips of lemon zest.
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Recipes like this appears in Appetizers, a special issue of party-perfect recipes from the editors of Fine Cooking, including extraordinary dips, wraps, crostini, and sweet bites.