Heat oven to 375° F. Line a 9-inch square baking pan with parchment paper.
With an electric mixer on medium-high, beat the butter, brown and granulated sugars, corn syrup, and vanilla for 3 minutes. Add the egg and beat until combined. In a separate bowl, whisk together the flour, salt, and baking soda. Reduce mixer speed to low and slowly add the flour mixture to the egg mixture. Stir in the cranberries, pecans, and rum.
Spread the batter into prepared pan. Bake for 35 minutes. Transfer pan to a wire rack. Cool for 10 minutes before slicing.