• Preheat the oven to 350℉. Line a cupcake pan with 10 paper liners and set aside.

Make the cupcakes:

• Combine strawberries and 1 teaspoon sugar in a large bowl. Transfer to a 9-inch pie plate and roast in the oven for 45 minutes, stirring once halfway. Remove from the oven and let cool for 5 minutes. Purée in a blender until smooth and set aside.
• Sift together flour, baking powder, and salt. Set aside.
• In a mixer fitted with the paddle attachment, cream the sugar, butter, lime zest, and vanilla on medium speed until light and fluffy, about 2minutes. Mix in eggs one at a time, scraping well after each addition. With the mixer on low speed, add the evaporated milk and flour mixture alternately, beginning with evaporated milk and ending with flour mixture. Mix in strawberry purée and rum. Scrape the bowl well.
• Scoop the batter into the cupcake liners, filling them up to the rim. (I use a 2.6-ounce ice cream scoop.) Bake in the center of the preheated oven until an inserted toothpick comes out clean, 18 to 20 minutes. Cool cupcakes for 10 minutes, then remove from the pan and allow to cool completely on a wire rack.

Make the frosting:

• Grind freeze-dried strawberries in a food processor to a fine powder. Sift to remove any larger bits.
• Beat together strawberry powder and butter in a large bowl with an electric mixer until smooth and creamy. Add powdered sugar, evaporated milk, vanilla, and salt. Beat on low speed until mixture begins to come together. Increase speed to medium and continue mixing until frosting is fluffy, about 2 minutes.
• Transfer frosting to a piping bag with the desired tip and swirl onto the cooled cupcakes. Garnish with fresh strawberries and lime zest if desired.