Heat the berries and 3/4 cup of the sugar in a 4-quart saucepan over medium-high heat, stirring occasionally, until they start to release juice but are still whole and intact, about 5 minutes. Stir in the ginger and pour the mixture onto a rimmed baking sheet to cool.
Meanwhile, in a large bowl, toss the bread with 5 Tbs. of the liqueur. In a chilled metal bowl with chilled beaters, whip the cream with the remaining 3 Tbs. liqueur and 1 Tbs. sugar to almost-stiff peaks.
In a 2- to 2-1/2 -quart clear glass bowl, layer in the following order: 1 mounded cup of bread cubes, 1 cup of berries and juices, and 1 cup of whipped cream. Repeat 3 times—you should have 12 layers total. For the final layers, use all the remaining bread, berries (and their juices), and whipped cream.
Cover and refrigerate until the juice has completely softened the bread, at least 4 hours or overnight. Garnish with fresh berries before serving.
This easy trifle is the perfect dessert for any backyard barbecue, whether you're serving chicken, burgers, or ribs. Visit the Guide to Grilling to get more recipes for your barbecue or cookout.