Preheat oven to 350F. Line a 12 slot cupcake pan with liners.
In medium bowl, whisk 1 1/4 cups low FODMAP flour, 1 1/4 tsp baking powder, and 1/2 tsp salt.
In a separate bowl, beat 3/4 cup sugar and 1/2 cup unsalted butter on medium until combined and thick. This may take a few minutes and make sure the butter is softened.
In the sugar/butter mixture, add one egg and beat in thoroughly, then add in the final egg and beat thoroughly. Finally, add in 3 tsp pure vanilla extract and mix until combined.
Begin adding the flour mixture into the sugar mixture in thirds. After each addition, add in a third of the buttermilk being used and mix. Alternate adding the flour and buttermilk until the mixture is a smooth and mixed batter.
Line the cupcake pan, filling up each slot 2/3s full.
Bake on 350F for 20-23 minutes, testing with a toothpick for doneness. The toothpick should insert and pull out without any residue on the toothpick.
Once done, pull out and allow to cool 5-10 minutes before frosting.