In a small saucepan over medium heat, slowly heat the milk and lemon verbena leaves until steaming but not boiling. Turn off the heat and cover to steep for 1 hour.
Strain out the leaves and set the milk aside.
In a separate bowl, whisk together cornstarch and sugar. Add eggs and whisk until smooth. Set aside.
In a saucepan, heat the milk and vanilla bean paste over medium-high heat until just below boiling. Stir occasionally.
Slowly add 1/3 of the hot milk to the egg mixture, whisking constantly to avoid cooking the eggs. Pour the egg-milk mixture back into the remaining hot milk. Whisk over medium heat until thickened, just below boiling. Remove from heat and strain through a sieve into a bowl.
Cool for 5-10 minutes, stirring occasionally, then mix in butter one piece at a time until smooth.
Cover the pastry cream with plastic wrap pressed directly onto the surface and chill in the refrigerator.
#### Tart Crust:
Preheat oven to 350°F.
Whisk together egg yolk, cream, almond extract, and vanilla. Set aside.
In a food processor, pulse together flour, sugar, and salt. Add chilled butter pieces and pulse until the mixture resembles coarse crumbs.
While the processor is running, add the egg mixture and process until the dough forms a ball.
Wrap the dough in plastic wrap and refrigerate for at least 1 hour.
Roll out the dough into an 11-inch circle and place it in a 9-inch tart pan. Press the dough into the bottom and sides of the pan, trimming any excess.
Line the tart with parchment paper and fill with pie weights or dried beans. Bake for 20 minutes, then remove weights and parchment. Prick the bottom with a fork and bake for another 15-20 minutes until golden brown. Cool completely.
#### Assembling the Tart:
Pour the cooled custard into the cooled tart shell, spreading it evenly with a spatula.
Heat and strain the apricot jam.
Arrange thinly sliced peaches on top of the custard and brush with the apricot jam.
Chill the tart in the refrigerator until ready to serve.
