Cream Cheese Frosting

Make the custard: In a 3-quart stainless steel saucier, bring the milk and vanilla bean to a simmer over medium heat. Remove from heat, cover and steep for 30 minutes. Alternatively cover and refridgerate for up to 24 hours to extract the deepest vanilla flavor

Whisk the sugar and cornstarch together in a medium bowl, followed by the eggs

Return the milk to a simmer. Remove vanilla bean, scrape the flavorful pulp into the milk, and discard the pod. Lade 1/2 cup of hot milk into the eggs, whisking to combine. Repeat with a second and third ladleful then pour the warmed eggs into the pot and cook over medium heat whisking constantly, until the custard turns thick and lumpy, about 3 minutes.

Once it begins to bubble sluggishly, continue cooking and whisking for 2 full minutes, to neutralize a starch-dissolving portein found in the yolks; the custard should be very smooth. Remove from heeat and stir in vanilla extract

Pour the custard into a baking dish about 7-by-11 inches to speed the cooling process. Press a sheet of plastic against the surface and refridgerate until thick and cool, about 1 hour (or roughly 68°F). Alternatively, refridgerate for up to 1 week, then let stand at room temperature until warmed to 68°F before proceeding

Finish the buttercream: In the bowl of a stand mxer fitted with the paddle attachment, beat the cream cheese and butter on medium speed until fluffly and light, about 5 minutes. Meanwhile, stir the thick pudding until smooth. Scrape the bowl and beater with a flexible spatula, then switch to the whisk attachment. Whipping on medium speed, add pudding a few tablespoons at a time, then drizzle in the lemon juice.

Scrape the bowl once more and whip for a few seconds to ensure that no lumps remain. The buttercream should be light and creamy, but thick enough to hang upside down from a spoon.