Preheat your oven to 350°F (175°C). Line a 9x13 pan with parchment paper, leaving a little overhang to lift the finished bars out easily.

In a large bowl, cream the softened butter and sugar until light and somewhat fluffy (about 2–3 minutes with a hand mixer).

Add eggs one at a time, mixing well after each, then stir in the vanilla.

In a separate bowl, whisk together flour, baking powder, and salt.

Alternately add the dry mix and milk to the butter mixture, beginning and ending with the dry ingredients. Mix until just combined.

Spread the batter evenly into your prepared pan.

Bake for 12–15 minutes, or until the edges are set and the center is slightly firm but not browned.

In a medium saucepan, heat the milk over medium heat until it just begins to steam (you’ll see tiny bubbles at the edge). Do not boil.

In a bowl, whisk the egg yolks, sugar, and cornstarch until smooth and pale.

Temper the yolks: slowly pour about 1/3 of the hot milk into the yolk mixture while whisking constantly.

Pour the yolk mixture back into the saucepan with the remaining milk. Cook over medium-low heat, stirring constantly, until the custard thickens and coats the back of a spoon (about 5–7 minutes).

Remove from heat, stir in butter and vanilla, and let cool for 5 minutes.

Pour the warm custard over the partially baked cake base, spreading it evenly.

Return to the oven and bake another 12–15 minutes, or until the custard is set at the edges and slightly jiggly in the center.

Allow the bars to cool to room temperature, then chill in the fridge for at least 2 hours to fully set.

Lift the bars from the pan using the parchment overhang, dust with powdered sugar or drizzle a light glaze if desired, and cut into bars.