01 - Preheat the oven to 350°F. Grease a 9-inch tart tin with removable base thoroughly.
02 - Rub the chilled butter into the flour, sugar, and salt in a bowl until the mixture resembles coarse breadcrumbs. Add the egg yolk and 2 tablespoons cold water, mixing until a dough forms. Add additional water only if needed for proper consistency. Wrap the dough in plastic and refrigerate for 20 minutes.
03 - Roll out the chilled pastry on a lightly floured surface and line the prepared tart tin. Trim excess pastry from edges. Prick the base thoroughly with a fork. Line with parchment paper and fill with baking beans or pie weights. Blind bake for 15 minutes. Remove beans and parchment, then bake for an additional 5 minutes until the crust is lightly golden.
04 - Combine apples, sugar, lemon zest and juice, cinnamon, and butter in a saucepan. Cook over medium heat, stirring frequently, until apples are tender but still maintain some shape, approximately 10 minutes. Remove from heat and allow to cool slightly.
05 - Whisk the egg yolks into the slightly cooled apple mixture until thoroughly combined. Spoon the apple filling evenly into the baked pastry case.
06 - In a clean, dry bowl, whisk egg whites with cream of tartar until soft peaks form. Gradually add sugar while continuing to whisk until stiff, glossy peaks develop. Fold in vanilla extract.
07 - Spoon or pipe the meringue over the apple filling, creating decorative peaks and ensuring the filling is completely covered.
08 - Bake for 20-25 minutes until the meringue peaks are golden and crisp to the touch.
09 - Allow the tart to cool completely in the tin before slicing. Serve slightly warm or at room temperature.