For the cupcakes: Preheat the oven to 350 degrees F. Line one 12-cup standard muffin tin with cupcake liners.
Whisk together the flour, granulated sugar, baking powder, milk, butter, vanilla, salt and egg in a medium bowl just until combined. Be careful not to over mix. Pour into the liners. Bake until a toothpick inserted in the center of the cakes comes out clean, about 18 minutes. Cool on a rack 10 minutes, and then remove the cupcakes and cool on the rack completely.
For the filling: Melt the butter in a 10-inch nonstick skillet over medium heat. Add the pineapple, sugar and salt and cook, stirring frequently, until caramelized and the liquid is mostly evaporated, 18 to 20 minutes. (You will be able to run your spoon through the filling and leave a streak behind that holds 1 to 2 seconds before filling back in. The consistency of the filling should be like caramel sauce.) Set aside to cool.
For the icing: Melt the butter in small saucepan over medium-low heat. Bring to a simmer and continue cooking until dark golden and toasty smelling, about 4 minutes. Once you see the milk solids turning a medium brown color, turn off the heat. Cool to room temperature. Whisk in the confectioners' sugar and pineapple juice to make it smooth but not too spreadable.
To assemble: Using a melon baller, scoop out a hole in each cupcake large enough for 1 tablespoon of pineapple filling. Fill and press gently with the back of the spoon to level the filling. Spoon a teaspoon of icing over the hole to cover. Garnish the cupcakes as desired with cherries and pineapple.