Put the 1/2 cup plus 1 tablespoon milk and 3 tablespoons plus 3/8 teaspoon dried lavender flowers in a measuring cup, cover, and refrigerate for a few hours, or overnight if possible. Do the same with the 2 tablespoons milk and 1 tablespoons lavender flowers for the frosting, but in a separate cup.
Preheat the oven to 375 (F) -- this is a 50-degree (F) increase from the original sea-level recipe temperature of 325 (F).
Put 1 cup flour, a scant 3/4 cup sugar, 1 teaspoon baking powder, and 3 tablespoons unsalted butter in a freestanding electric mix with a paddle attachment (or use a handheld electric whisk) and beat on slow speed until you get a sandy consistency and everything is combined.
Strain the lavender-infused milk for the cupcake (the 1/2 cup plus 1 tablespoon milk measure) and slowly pour into the flour mixture, beating well until all the ingredients are well mixed.
Add the egg and beat well, scraping any unmixed ingredients from the side of the bowl with a rubber spatula.
Spoon the batter into paper cases in your muffin tin until two-thirds full, and bake in the preheated oven for 20-25 minutes, or until the cake bounces back when touched. A skewer inserted in the center of the cupcakes should come out clean.
Let the cupcakes cool slightly in the pan before turning out onto a wire rack to cool completely.