Make the cake Position a rack in the center of the oven and heat the oven to 350°F. Butter a 9x13-inch baking pan and line the bottom with parchment.
In a medium bowl, whisk the flour, ginger, baking soda, salt, allspice, cinnamon, and white pepper.
Beat the butter, sugar, and lemon zest in a stand mixer fitted with the paddle attachment (or in a large bowl with an electric hand mixer), on medium-high speed until light and fluffy, about 2 minutes. Add the eggs, one at a time, beating well after each addition. Mix in the molasses. Add half of the dry ingredients and mix on low speed until just combined. Add half of the milk and mix to combine. Repeat with the remaining dry ingredients and milk.
Scrape the batter into the prepared pan, smooth the top, and bake until the center of the cake bounces back when lightly pressed and a cake tester comes out clean, about 25 minutes. Cool on a wire rack for about 20 minutes; then carefully invert the cake onto the rack and let it cool completely.
Make the ginger-tea syrup In a small saucepan, combine the sugar and ginger with 1/2 cup water. Bring to a simmer over medium heat and simmer for 15 minutes. Strain the syrup through a fine sieve set over a small bowl, pressing on the ginger to extract all of the syrup. Add the tea bag to the hot syrup and cool completely. Remove the tea bag and add the brandy.
Make the filling Pour 2 to 3 inches of water into a medium saucepan and bring to a simmer over medium heat. In a medium stainless-steel bowl, whisk the sparkling wine, egg yolks, sugar, and 2 Tbs. of the ginger syrup.
Set the bowl over the simmering water, making sure the bottom doesn’t touch the water. Whisk constantly until you can see the bottom of the bowl when you scrape the whisk across it, and the mixture is the consistency of pudding, about 8 minutes. Immediately remove from the heat and whisk frequently until cool.
Meanwhile, beat the heavy cream in a large bowl with an electric hand mixer on medium high speed until it just starts to thicken. With the mixer still running, add the vanilla and 1 Tbs. of the ginger syrup. Continue beating until medium peaks form, about 2 minutes.
Whisk the mascarpone into the cooled egg mixture. With a spatula, gently fold the egg mixture into the whipped cream.
Assemble the trifle Cut the cake into 1-inch cubes. Spoon a rounded cup of the filling into the bottom of a 7-1/2-inch-diameter, 14-cup (or similar) trifle dish. Arrange a third of the cake on top of the filling in an even layer. Drizzle 1/4 cup of the ginger syrup over the cake. Scatter 1 Tbs. of the candied ginger over the cake.
Repeat this layering 2 more times. Spoon the remaining filling over the final layer and smooth with the spoon. Sprinkle the remaining 3 Tbs. candied ginger over the top.
Cover tightly with plastic wrap and refrigerate for at least a day.
Serve Remove the trifle from the refrigerator 1 to 2 hours prior to serving. Use a large spoon to scoop servings into individual dishes.
