Make pastry: In a bowl, whisk together flour, sugar, salt, and lemon zest. Scatter butter over flour mixture and, using your fingers, work it into flour until mixture is the consistency of coarse cornmeal. In a bowl, stir together 1 tbsp. water and the vanilla. Drizzle vanilla mixture over flour-butter mixture and stir with a fork until evenly moistened. Gather dough into a ball, wrap in plastic wrap, and let rest 30 minutes.
Press pastry evenly onto bottom and up sides of a 9-in. round tart pan with a removable rim. Line tart shell with foil and place in the freezer 30 minutes. Preheat oven to 375°.
Fill tart shell with pie weights or dried beans and bake until light golden brown, 15 to 20 minutes. Remove pie weights and foil and continue to bake until tart shell is baked all the way through, about 5 minutes longer. Let cool completely on a cooling rack.
Make pastry cream: In a heavy saucepan, combine milk and salt over medium-high heat and heat until small bubbles appear along edges of pan. Meanwhile, in a bowl, whisk together cornstarch and sugar. Add eggs and whisk until smooth. Slowly drizzle half of milk into egg mixture while whisking constantly. Pour egg-milk mixture back into saucepan of hot milk, return pan to medium heat, and continue cooking, whisking constantly, until custard thickens, about 2 minutes (do not boil). Remove from heat and pour through a fine-mesh strainer into a bowl. Stir in kirsch and let cool 10 minutes, stirring occasionally. Add butter and stir until combined. Cover bowl with plastic wrap, pressing wrap directly onto top of pastry cream, and refrigerate until well chilled, about 2 hours.
Spread pastry cream evenly into tart shell. Halve strawberries. Starting at edge of shell, arrange berries, cut side down, in tight concentric circles, covering pastry cream nearly completely.
In a saucepan, combine jam and 1 tbsp. water over medium-low heat and stir until jam liquefies. Brush berries with jam. Let set 20 minutes before serving.