Preheat oven to 350ºF. Line a 12-muffin tin with paper liners.
Sift the flour into a medium bowl. Add the baking powder and salt and stir to combine. Set aside.
Prepare the wet ingredients:
In a large bowl, combine the butter and sugar. Using an electric mixer, beat the sugar and butter until it is pale and fluffy, about 2-3 minutes total.
Add the egg, mixing thoroughly after each addition. Add the vanilla and crème fraîche and mix until combined.
Combine the wet and dry ingredients:
Add half the flour and mix until combined. Add the remaining flour and continue mixing until it is combined. Be careful not to overwork the mixture.
Bake the cupcakes:
Spoon the mixture into the muffin liners in the tin, filling each muffin liner up about 3/4 of the way. Use the back of a teaspoon to smooth out the tops of each cupcake.
Transfer to the oven for 20-24 minutes or until a toothpick poked in the center of the cupcake comes out clean.
Cool the cupcakes:
Transfer the vanilla cupcakes to a wire rack and cool them completely, about 1-2 hours at room temperature.
Prepare the lemon buttercream:
Add the butter to a mixing bowl and, using an electric mixer, beat for 1-2 minutes until it is creamy. Sift half the powdered sugar into the bowl and mix until incorporated.
Sift the remaining powdered sugar into the mixture along with the lemon juice and zest, vanilla extract, and milk. Mix on high for 3 minutes or until the mixture is creamy and fluffy. If the buttercream seems stiff, add a splash of cream or milk. If it is too loose, add a spoonful or two of powdered sugar until it reaches your desired consistency.
Ice the cupcakes
Ice the cupcakes using a piping bag, butter knife, or makeshift piping bag (ziplock bag with the bottom right corner snipped off). Enjoy!
Notes
*Cupcakes should be stored in an airtight container. They will be good for 2 days at room temperature or 5 days in the fridge.