Set out the egg, egg yolk, butter and sour cream about 30 minutes ahead of time so they come to room temperature.
Weigh the flour on a kitchen scale.
Preheat the oven to 175°C.
Line the 12 cups of a muffin pan with paper liners.
12 paper liners
Batter
Put the flour, sugar, baking powder, baking soda and salt in the bowl of an electric mixer.
140 g cake flour, 144 g granulated sugar, 0.75 teaspoon baking powder, 0.25 teaspoon baking soda, 0.25 teaspoon salt
Mix on low speed for about 20 seconds.
Add the softened butter and the oil.
57 g butter, 3 tablespoons vegetable oil
Mix for 1 to 2 minutes, until the flour is coated with fat and the mixture looks like wet sand.
In a small bowl, whisk the egg, egg yolk, vanilla and sour cream until smooth.
1 large egg,, 1 large egg yolk,, 1 tablespoon vanilla extract,, 120 g sour cream,
On low speed, slowly pour this wet mixture into the mixer bowl.
Scrape down the bottom and sides of the bowl.
Switch to medium speed.
Beat for about 1 minute, until the batter is smooth.
Baking
Divide the batter among the liners, filling them about two-thirds full.
Bake for 16 to 20 minutes, until a toothpick inserted in the center of a cupcake comes out clean.
Take the cupcakes out of the oven.
Set the cupcakes on a wire rack.
Let them cool completely before frosting.
Vanilla Buttercream
With an electric mixer, beat the softened butter on medium-high speed for 2 to 3 minutes, until light and creamy.
115 g butter
Add the vanilla and salt.
1.5 teaspoons vanilla extract, 1 pinch salt
Beat until incorporated.
Add half the powdered sugar, starting on low speed and then moving up to medium, until it is fully incorporated.
225 g powdered sugar,
Add the rest of the powdered sugar the same way.
Scrape down the bottom and sides of the bowl as needed.
Add the cream one tablespoon at a time until you reach the consistency you want.
2-3 tablespoons cream
Scrape down the bottom and sides of the bowl.
Add the food coloring, if desired.
Food coloring,
Switch to medium-high speed.
Beat for another 3 to 5 minutes, until the buttercream is smooth, light and fluffy.
Frosting
Frost the completely cooled cupcakes with the buttercream.
Notes
Method: this recipe uses what is known as the “two-stage” method (reverse creaming). You first coat the flour with fat before adding the liquids, which limits gluten development: the crumb is more tender and velvety, and the batter comes together in a single bowl. The cupcakes bake up with a nice dome, without sinking or spilling over. The classic method, where you beat the butter and sugar first, gives a more pronounced dome.Moistness: the oil, the extra egg yolk and the sour cream keep the cupcakes moist. Frosted and then kept in an airtight container, they are still moist the next day. Store them for up to 2 days at room temperature in an airtight container, not in the fridge, which dries them out.Flour: American cake flour is a low-protein flour that gives a light crumb that doesn't sink. In France, T45 flour is the closest match. Failing that, use T55 flour and replace about 15% of it with cornstarch (Maïzena), which comes to roughly 120 g of T55 and 20 g of cornstarch.Sour cream: in Germany, saure Sahne or Schmand. In France, you can sometimes find it in the refrigerated section; otherwise, use thick crème fraîche.Oil: a neutral oil, sunflower or canola.Cream for the buttercream: heavy cream, or milk if you don't have any.For even lighter cupcakes, you can separate the egg, beat the white to stiff peaks and gently fold it into the batter at the end.Mini cupcakes: allow about 10 minutes of baking time.Piping: for the classic swirl of American bakeries, use a piping bag fitted with an open star tip (such as a Wilton 1M or Ateco 828). The buttercream should be soft enough to pipe through the tip without tearing, and firm enough to hold its shape without slumping: adjust with the cream, a few drops at a time. In a warm kitchen, put the buttercream in the fridge for a few minutes before piping. As it air-dries, American buttercream forms a thin crust that keeps the ridges defined.Chocolate variation: these vanilla cupcakes also pair well with an American chocolate buttercream. Chocolate cupcakes are a different recipe: there, you dissolve unsweetened Dutch-process cocoa in 120 to 240 ml of boiling liquid to bring out its flavor.