Preheat oven to 350 degrees F. Line a mini cupcake pan with papers.
In a large mixing bowl, add in the olive oil and sugar. Mix on medium until combined.
Add in the vanilla and eggs one at a time. Once the first egg is completely incorporated, add in the next egg. Mix until incorporated. Scrape down the sides.
Add in the sour cream and mix on medium until combined.
Add in the cocoa powder, flour, baking powder, baking soda and salt. Mix on low until the flour is just incorporated. Scrape down the sides and stir in any remaining flour.
Scoop the batter into the cups. Fill about ⅔ full with batter.
Add a mini peppermint patty to the center of each cupcake. I stood them on their side and not flat.
Place in the oven and bake for 10 minutes or until done. Place a toothpick off to the side of the candy. If it comes out with moist crumbs or clean, it's done. If there's still batter, let it bake an additional minute or two.
Let the cupcakes cool completely.
In a large mixing bowl, add in the butter. Mix on medium until it's creamed.
Add in the powdered sugar, heavy cream, and peppermint extract. Beat on low until the powdered sugar is incorporated.
Once the powdered sugar is incorporated, beat on high for 2 to 3 minutes until light and fluffy.
Place the frosting in a piping bag with a 1M tip. Pipe a swirl on each cooled cupcake.
Add some white sprinkles and a mini peppermint patty to the top of frosted cupcakes.