Get out a small and a medium sized sauce pan.
In small sauce pan, boil milk. Remove from heat.
In large sauce pan, mix egg yolks, sugar and corn starch. Incorporate on low heat, adding in 1/4 cup of hot milk. Continue whisking (an electric beater with a whisk wand works like a charm), and gradually add in remaining milk, boiling mixture for one minute. Immediately remove from heat.. Add in vanilla. Allow to sit for five minutes.
Add butter. Cool completely, before assembling.
Wash and rinse fruit well, removing all stems. Dry fruit.If blackberries are very tart, add 1 - 2 tablespoons of sugar and allow to sit for an hour at room temperature. Add raspberries at very end, as they are more delicate.
Spread pastry cream onto tart crust.
Top with berries of your choice. Heat preserves or jam with 1 tablespoon of water. Brush fruit with pastry brush. Refrigerate. You can make this one day ahead. I like to make the cream and the tart crust the day before and assemble a few hours before serving.
Top with lime basil.