Step 1Adjust an oven rack to the lower-third position and heat the oven to 350 degrees. Line 14 muffin cups with paper liners; set aside.
Step 2Resift the flour with the baking soda, salt, ground ginger and allspice; set aside.
Step 3In a large bowl, beat the butter with an electric mixer on medium speed until smooth, about 1 minute. Add the vanilla, fresh ginger, orange zest and one-fourth cup of the brown sugar. Beat for 1 minute. Beat in the remaining three-fourth cup brown sugar about one-fourth cup at a time, beating for about 20 seconds after each addition. Scrape the bowl and beaters and beat on medium-high speed for 4 minutes until smooth and fluffy. Add the egg and beat 1 minute.
Step 4On a low speed, add the flour mixture in 3 additions, alternating with the buttermilk, beginning and ending with the flour and beating only until smooth after each addition. Stir in the crystallized ginger. Divide the batter evenly among the muffin cups, filling them about two-thirds full. Don't bother to smooth the batter; it will level itself during baking.
Step 5Bake until the cupcakes are golden brown and spring back when gently pressed in the center, about 25 minutes. Cool in the pans for 5 minutes, then remove them to wire racks. Cool completely before frosting.
Step 1While the cupcakes are cooling, heat the cream in a small heavy saucepan over medium heat until it just comes to a boil. Remove from the heat and add the white chocolate. Whisk until the chocolate is melted and the mixture is smooth. Whisk in the sour cream. Set aside, whisking occasionally, until the frosting is completely cool and thickened enough for spreading.
Step 2Place a teaspoonful of frosting on top of each cupcake and spread evenly with the back of a spoon. Let stand until set before serving.