In a medium saucepan, combine cranberries, 2 cups granulated sugar, ginger, and 2 cups water. Bring to a simmer over medium; cook until cranberries begin to burst, 8 to 10 minutes. Let compote cool completely.
Make cream filling: Using an electric mixer, beat cream cheese, brown sugar, remaining cup granulated sugar, and vanilla on high until well combined. With mixer on medium, gradually add heavy cream; continue beating until soft peaks form.
Arrange 1/3 of cake in a 3-quart serving dish. Spoon 1/3 of compote over cake; spread to sides of dish. Dollop 1/3 of cream filling over compote; spread to sides of dish. Repeat twice, ending with cream filling. Cover; refrigerate at least 2 hours (or up to 1 day). Garnish with Candied Orange Zest, if desired.
In a medium saucepan, bring 1/2 cup and 1/2 cup to a boil, stirring to dissolve sugar. Add (peeled into long strips with a vegetable peeler); simmer, swirling occasionally, until zest is tender, 8 to 10 minutes. Drain, and transfer to a plate. Dredge zest in sugar, and thinly slice.