Preheat your oven to 350°F. Line your muffin pan with cupcake liners and set aside.
In a mixing bowl, cream together the butter and sugar on medium speed for 2–3 minutes until smooth and fluffy.
Add in the egg, Rumchata, and vanilla extract. Mix on medium-low speed until fully incorporated.
Stir in the cinnamon, salt, baking powder, and flour. Mix on low until the batter is well combined, scraping the bowl as needed.
Divide the batter evenly among the cupcake liners, filling each about ⅔ full. In a small bowl, mix the sugar and cinnamon, then sprinkle about ½ teaspoon onto each cupcake.
Bake for 15 minutes, or until the centers are set.
Make the frosting by combining the softened butter, vanilla, salt, Rumchata, and powdered sugar.
Mix on low until everything is combined, then increase to medium speed and beat for 2–3 minutes until light and fluffy.
Transfer the frosting into a piping bag fitted with a large star tip. Pipe a generous swirl of frosting onto each cupcake, then sprinkle with the remaining cinnamon sugar.