Make tart: In a large bowl cream butter and powdered sugar with a hand mixer about 1-2 minutes. Add the egg and egg yolk, mix together for 1 minute. In a bowl mix, together kosher salt and flour. Slowly add the flour and mix on low speed until a dough ball forms.
On a lightly floured, press dough into a disc shape, roll out to a 12-inch circle that’s 1/8 inch thick. Transfer dough to a buttered tart pan. Press dough into pan, making sure the dough is smooth against pan. Roll your rolling pin over the top to secure the top of the dough. Discard the scraps of dough. Use a fork to prick the dough evenly, wrap with plastic wrap and place in freezer for 30 minutes.
Make pastry cream: In a bowl mix, flour, cornstarch, sugar and salt. In a bowl whisk, eggs yolks. Then add to flour mix, and whisk until it resembles wet sand.
Turn on the heat to medium in a medium pot add the half and half, bring to a slight boil, about 3-5 minutes. Once mixture is slightly boiling, whisk a 1/3 into the egg-flour mix. Pour back into the pot, stirring constantly, cook until custard thickens. Once custard looks lumpy increase speed of stirring, until smooth. Allow cream to boil for 10 seconds.
Strain pastry cream in a fine mesh strainer over a bowl, stir in lemon extract, lemon zest and butter. Place plastic wrap directly on pastry cream, then place over an ice bath for 30 minutes to cool.
While pastry cream cools. Preheat the oven to 350°F. Add the tart to a baking sheet and pop in the oven for 12 minutes or until golden brown. Remove and cool for 10 minutes. At this point the tart is ready for it filling.
Fill the cooled tart evenly with pastry cream. Arrange berries over pastry cream in an even layer, fully covering the pastry cream. Brush the fruit with melted apricot for a glossy covering. Cover with plastic wrap and pop in the fridge for 4 hours to overnight. Tart is good for up to 4 days in the fridge.