Position a rack in the lower third of the oven and heat the oven to 350°F. Lightly butter the bottom and sides of a 9-inch round cake pan with sides at least 2-1/2 inches high. (A springform pan will work; just be sure to set it on a foil-lined baking sheet to catch any leaks.)
Put 4 Tbs. of the butter in the buttered pan. Put the pan in the oven until the butter melts, about 5 minutes. Remove the pan from the oven and stir in the brown sugar and cinnamon until well combined. Spread the brown sugar mixture evenly over the bottom of the pan and spread the cranberries evenly over the sugar.
Put the remaining 12 Tbs. butter in a medium bowl. Using a wooden spoon, cream the butter with the granulated sugar and egg yolk until blended, about 20 seconds. Switch to a whisk and stir in the eggs one at a time. Whisk until the batter is smooth and the sugar begins to dissolve, about 30 seconds. Whisk in the sour cream, vanilla, and salt. Sift the cake flour, baking powder, and baking soda directly onto the batter. Using the whisk, combine the ingredients until the mixture is smooth and free of lumps.
Spread the batter evenly over the cranberry mixture in the cake pan. Bake until the center of the cake springs back when gently touched and a skewer inserted in the center comes out with only moist crumbs clinging to it, 50 to 65 min. Set the pan on a rack to cool for 5 to 10 minutes (the cranberry syrup in the bottom of the pan will be too thick if you wait longer). Run a knife between the cake and sides of the pan. Invert the cake onto a serving plate and remove the pan. Let cool for at least 15 min. more before serving. This cake is best served warm and fresh.