Start by preheating your oven to 325°F then place paper liners in 2 12-cup muffin pans. You will need 4 more so you can wait until a batch of cupcakes bake before lining with the remaining ones.
In your mixer bowl, add oil and butter and beat for 2 minutes on high speed. Slowly add in sugar and beat on high speed for an additional 4-5 minutes until very pale yellow and fluffy. Next, add eggs, one at a time, combining well after each addition and scraping down the sides as needed.
Turn your mixer down to its lowest speed, and slowly add flour into batter in two increments then add baking powder, salt and baking soda. Be careful not to over beat.
Lastly, add sour cream, milk, lime zest, lime and vanilla extracts, scrape down sides and mix until just combined and turn off mixer.
Evenly pour batter into prepared muffin pan liners filing three-quarters of the way full. Place the pan on a baking sheet and bake for 17 to 19 minutes or until completely set in the center. Let cool completely to room temperature before adding any frosting.