Lightly brush a 9-inch springform pan with vegetable oil. In a food processor, pulse the graham crackers, brown sugar and cinnamon to fine crumbs. Add the butter and process until the crumbs are moistened. Press the crumbs over the bottom of the pan and refrigerate until firm, 30 minutes.
In a bowl, beat the goat cheese with the lemon juice until creamy. Add the cream and beat until the mixture is very firm, about 3 minutes. Add 1/3 cup of the granulated sugar; beat until the mixture is smooth and slightly softened, about 2 minutes. Pour the batter over the crust. Refrigerate until well chilled, at least 5 hours or preferably overnight.
In a saucepan of boiling water, simmer the orange zest over moderate heat for 10 minutes. Drain and return to the saucepan. Add the remaining 1/4 cup of granulated sugar and stir over low heat until the sugar is melted and the zest is glazed, about 2 minutes. Stir in the vinegar and transfer the candied zest to a small bowl.
Rinse and dry the saucepan. Add the honey and bring to a boil. Remove from the heat, stir in the cranberries and let cool.
Run a small, thin knife around the edge of the springform pan and remove the ring. Using a hot knife, trim the cake to a 6-inch square (serve the trimmings as snacks), then cut into 10 rectangles. Alternatively, cut the cake into wedges. Transfer to plates, garnish with the orange zest and honeyed cranberries and serve.