Make gingerbread: Preheat oven to 350°. Butter an 8- by 8-in. baking pan. In a medium bowl, mix flour, baking soda, cinnamon, 1 teaspoons ground ginger, the cloves, and 1/2 teaspoons salt. In a large bowl, whisk 3/4 cup granulated sugar with 1 egg until thick and pale.
Stir in applesauce, molasses, 1 tablespoons fresh ginger, oil, and 1/4 cup hot water. Stir in flour mixture.
Pour into pan and bake until a toothpick inserted in the center comes out clean, about 35 minutes. Let rest 5 minutes; turn out onto rack and let cool. Cut into 1-in. cubes.
Cook pears: Melt 2 tablespoons butter in a frying pan over medium heat. Add pears. Cook, stirring, until soft, 7 minutes.
Stir in brown sugar, 1/2 teaspoons ground ginger, and 1/4 teaspoons salt.
Make custard: In a pan over medium heat, whisk half-and-half, 3 eggs, 1/2 cup granulated sugar, cornstarch, and 1/4 teaspoons salt until thickened, 10 minutes. Take off heat; stir in vanilla and 2 tablespoons butter.
Whip cream: In a large bowl, beat cream, powdered sugar, and remaining 1/2 teaspoons fresh ginger until soft peaks form.
5. Assemble trifle: Put half the gingerbread cubes in a trifle dish or glass bowl. Sprinkle with half the brandy. Spoon half the pears and liquid over gingerbread. Pour half the custard over pears. Top with half the whipped cream and half the crystallized ginger. Repeat layers. Serve immediately, or cover and chill up to 1 day.