In a medium skillet, melt the butter over medium-low heat. Stir in the pretzels and 2 tablespoons sugar and cook until lightly toasted, about 3 minutes. Transfer to a bowl to cool slightly. Press about 2 tablespoons into the bottom of each cup of a 12-cup muffin pan. Freeze for 30 minutes.
Meanwhile, using an electric mixer, beat the cream cheese on medium speed, scraping down the sides of the bowl, until fluffy, 2 to 3 minutes. Mix in the remaining 1 1/4 cups sugar on low speed, then gradually mix in the lime peel, lime juice, rum and chopped mint.
In a separate bowl, beat the heavy cream until stiff peaks form. Fold into the cream cheese mixture.
Divide the cream cheese mixture evenly among the muffin cups; smooth the tops. Cover with plastic wrap and freeze for at least 8 hours or overnight.
To serve, run a wet knife around each cake, then invert the pan onto a clean work surface. Set each cake upright and top with a mint sprig.