Preheat oven to 180°C. Butter a 32 x 22cm baking pan. Line pan with parchment paper, letting excess extend over sides of pan.

In a medium bowl, whisk together milk, yoghurt, eggs, egg yolks, and vanilla extract.

In the bowl of a stand mixer fitted with the paddle attachment, beat flour, sugar, baking powder, and salt at low speed just until combined.

Add butter, one cube at a time, beating until combined after each addition.

Add half of milk mixture; beat at low speed just until combined.

Add remaining milk mixture, and beat at medium speed just until combined.

Using a rubber spatula, fold batter to ensure that no dry ingredients remain.

Pour batter into prepared pan, smoothing top with an offset spatula.

Bake until cake springs back when touched in centre and a wooden pick inserted in centre comes out clean, about 45 minutes.

Let cool completely in pan.

In the heatproof bowl of a stand mixer, combine egg whites, sugar, and salt.

Place bowl over a saucepan of simmering water, and cook, whisking constantly, until sugar dissolves and an instant-read thermometer registers 70°C.

Carefully return bowl to stand mixer. Using the whisk attachment, beat at high speed until white and fluffy, for approximately 8 to 10 minutes.

Add butter to mixture, one cube at a time, beating until combined after each addition.

Beat at high speed for 10 minutes.

Add vanilla bean paste to mixture, and beat at high speed for 2 to 3 minutes.

Switch to the paddle attachment, and beat at low speed for 1 minute to remove any air.

Using excess parchment as handles, remove cooled cake from pan.

Using an offset spatula, spread Vanilla Bean Swiss Meringue Buttercream onto cake, swirling as desired.

Garnish with sprinkles, if desired.