Mix flour, sugar, and salt in a large bowl. Cut in butter until crumbly. Add eggs and vanilla extract and combine into a dough ball. Wrap in plastic and refrigerate for 1 hour, up to 1 day.

While chilling dough, prepare filling: Toss apples with sugar and cinnamon in a medium bowl. Mix in chopped walnuts.

Preheat oven to 350°F (175°C). Grease sixteen 3-inch tart pans lightly. Let dough sit at room temperature for 30 minutes before rolling.

Knead dough briefly on a floured surface. Cut into 16 portions and roll each into a 6-inch circle.

Place dough circles into tart pans. Add filling evenly, fold pastry edges over filling, and arrange tarts on a baking tray.