8 tablespoons unsalted butter, room temperature
1 cup sugar
1/2 teaspoon ground cinnamon
1/4 teaspoon allspice
1 3/4 cups cranberries
1 large egg
1 teaspoon vanilla extract
1 1/4 cups all-purpose flour
1 1/2 teaspoons baking powder
1/4 teaspoon salt
1/2 cup milk
Preheat oven to 350 degrees with rack in center. Rub the bottom and sides of an 8-inch round cake pan with 2 tablespoons butter. In a small bowl, whisk together 1/2 cup sugar with the cinnamon and allspice. Sprinkle mixture evenly over bottom of pan; arrange cranberries in a single layer on top.
With an electric mixer, cream remaining 6 tablespoons butter and 1/2 cup sugar until light and fluffy. Add egg and vanilla; beat until well combined. In another bowl, whisk together flour, baking powder, and salt. With mixer on low speed, add flour mixture to butter mixture in three batches, alternating with the milk, until well combined.
Spoon batter over cranberries in pan, and smooth top. Place pan on a baking sheet; bake cake until a toothpick inserted in the center comes out clean, 30 to 35 minutes. Let cool on a wire rack for 20 minutes. Run a knife around edge of cake; invert onto a rimmed platter.