In a heat-safe bowl, combine egg yolks, sugar, and milk.
Fill a shallow pot halfway with water and bring the water to a simmer. Reduce the heat and set the heat-safe bowl with yolk mixture, cover the pot so that its sides are resting on the top half of the pot. (You can also use a double boiler pot if you have one.)
Whisk until the mixture is thickened. Remove and let it cool.
Whip heavy cream with vanilla extract as indicated on the package.
Stir mascarpone and whipping cream into the mixture.
Pour lemon juice and limoncello into a small bowl.
Dip each ladyfinger biscuit on both sides for a second or two in the lemon mixture, then arrange them on the bottom of the baking dish.
Cover the biscuits with a layer of the mascarpone mixture and level it well with a spatula.
Repeat the layers and finish with a layer of mascarpone cream.