Preheat oven to 350 degrees F. Line mini muffin pan with cupcake liners. Set aside.
In large bowl combine flour, baking powder, and salt, and mix well.
In large bowl with electric mixer, beat together butter and sugar until light and fluffy, about 2 minutes.
Add orange zest, and beat until combined.
Add eggs, one at a time, beating well after each addition.
Combine orange juice, milk, and vanilla in a small bowl.
Alternating with the flour mixture, add ⅓ of the milk/OJ mixture, mixing until combined, and then add ⅓ of the flour mixture.
Repeat this until mixture is all used.
Pour into prepared muffin tins, about ¾ of the way full.
Bake in preheated oven for 12-15 minutes, until a toothpick comes out clean.
To make the frosting:
Beat butter until light and fluffy, about 2 minutes.
Add orange juice, zest, extract, and 1 cup of powdered sugar.
Beat until well combined.
Add remaining powdered sugar 1 cup at a time, beating well after each addition.
Pipe onto completely cooled cupcakes
To make the candied oranges:
In saucepan, combine water and sugar over medium heat.
Stirring often, heat until sugar is completely dissolved.
Add orange segments, arranging them in a single layer. If your saucepan is too small to do all segments in one batch, do two batches.
Let them cook in the sugar water mixture for 25-30 minutes, or until they are candied.
Place them on wax paper and let them cool completely.
Top each cupcake with one segment.
Enjoy!