To make the brownies, position a rack in the bottom third of the oven. Preheat the oven to 350°F. Butter a 9x13-inch baking pan or spray it with nonstick spray. Dust with flour and tap out the excess. Set aside.
In a medium bowl, combine the flour, baking soda, and salt.
Place the chocolate in a heatproof bowl set over a pan of gently simmering water. Stir constantly until the chocolate is almost melted.
Remove the bowl from the heat and stir until the chocolate is completely melted.
In a large bowl, beat together the butter and sugar with an electric mixer until light and fluffy, about 3 minutes.
Add the eggs one at a time, beating well after each addition.
Add the melted chocolate and beat until well incorporated, about 2 minutes, scraping down the sides of the bowl as necessary.
With a wooden spoon or a spatula, gently stir the flour mixture into the chocolate mixture just until combined. Gently stir in the cola and the rum; then pour the batter into the prepared pan, smoothing it to the edges.
Bake the brownies until a toothpick inserted in the center comes out clean, about 35 minutes. Cool the brownies in the pan completely.
To make the frosting, in a large bowl beat the butter, cocoa powder, and rum with an electric mixer until smooth. Slowly add the confectioners' sugar, one cup at a time, beating until incorporated after each addition.
Spread the frosting over the cooled brownies.
Sprinkle with the grated lime zest, cut into squares, and serve.
