Line a standard 12-cup muffin pan with cupcake liners. In a medium bowl, sift together the cake flour, baking powder, baking soda, and salt. Whisk to combine thoroughly, ensuring leaveners are evenly dispersed to prevent uneven domes or air pockets in the finished cupcakes.

In the bowl of a stand mixer fitted with the paddle attachment, cream together the butter, oil, and sugar on medium-high speed for 2 to 3 minutes, until the mixture is light, fluffy, and noticeably paler. Proper creaming creates tiny air bubbles that contribute to rise and that classic soft crumb.

Add the egg, egg yolk, and vanilla bean paste to the creamed butter mixture. Beat on medium for 1 minute, scraping down the bowl once. The mixture should look satiny and slightly thickened, not curdled. This emulsifies fat and liquid and binds the structure for tender cupcakes.

Reduce mixer to low. Add one third of the dry ingredients, mixing just until faint streaks remain, then half the buttermilk. Repeat, ending with the final third of dry ingredients. Stop mixing as soon as the batter is mostly incorporated, then finish folding gently by hand. This minimizes gluten for a tender, moist crumb.

Use a cookie scoop or large spoon to divide the batter evenly among the liners, filling each about two-thirds full. Bake on the center rack of a preheated 350°F (175°C) oven for 17-19 minutes. The cupcakes are done when golden on top, springy to the touch, and a toothpick inserted in the center comes out with a few moist crumbs (not wet batter).

Remove the pan from the oven and let cupcakes cool in the pan for 5 minutes before transferring them to a wire rack. Cool completely to room temperature before frosting. This prevents the buttercream from melting or sliding, ensuring clean, tall swirls.

In a clean stand mixer fitted with the paddle (or whisk) attachment, beat the softened butter on medium-high for 3 minutes until smooth, shiny, and nearly white. Properly whipped butter traps air, vital for a buttercream that’s light while also sturdy for piping tall swirls.

With the mixer on low, gradually add the sifted powdered sugar until combined. Scrape down the bowl, then add vanilla bean paste, salt, and 2 tablespoons of heavy cream. Increase speed to medium-high and whip for 2 full minutes, adding more cream only if needed to achieve a glossy, fluffy frosting that holds peaks when piped.

Transfer the buttercream to a piping bag fitted with a large open star or round tip. Pipe tall swirls onto each cooled cupcake, holding the bag vertical and moving slowly for defined peaks. Buttercream should hold its shape without sagging or sliding. Finish with sprinkles if desired.