In a bowl, beat the butter with the sugar until fluffy. Beat in the egg yolk. Add the flour and salt; beat until a dough just begins to form. Transfer the dough to a work surface and roll into a log. Wrap the dough in plastic and refrigerate until chilled, about 1 hour.
Preheat the oven to 375°. Cut the dough into 8 pieces. On a lightly floured surface, roll out each piece to a 3-inch round. Transfer the rounds to eight 4-inch fluted tartlet molds with removable bottoms. Press the dough into the molds and up the sides. Refrigerate until firm, about 15 minutes.
In a mini food processor, pulse the almonds, flour, light brown sugar and zest until the almonds are coarsely chopped. Add the butter; pulse until the mixture resembles coarse meal.
Coarsely grate the apples and squeeze out the excess liquid. Transfer to a bowl and stir in the sugars, lemon juice, vanilla and cinnamon.
Using a fork, fill the tart shells with the apple mixture, leaving all the excess liquid in the bowl. Top the tartlets with the crumble. Transfer to a rimmed baking sheet; bake for about 35 minutes, until the crust is lightly browned. Serve.