Heat oven to 375° F. Line the bottom of a 9-inch springform pan with parchment or wax paper.
In a medium saucepan, combine the granulated sugar, 2 tablespoons of the brown sugar, the corn syrup, and 1/2 cup of the cream. Bring to a boil, then lower heat and simmer, stirring, until the sugar dissolves, about 2 minutes. Remove from heat and stir in the rum, salt, and pecans. Pour into the prepared pan and spread into an even layer. Bake until golden and set, about 40 minutes. Let cool for 30 minutes before slicing into wedges.
Whip the remaining cream and brown sugar until soft peaks form. Serve with the Pecan Wedges.