For the crust: In a food processor, pulse the flour and salt together. Add the chilled butter and pulse until the mixture resembles coarse crumbs. Slowly add the ice water, one tablespoon at a time, pulsing until the dough comes together. Turn the dough onto a floured surface, shape it into a disk, wrap it in plastic wrap, and refrigerate for at least 30 minutes.

1. For the filling: In a small saucepan, melt the butter over medium heat. Continue cooking the butter, swirling the pan occasionally, until it turns golden brown and smells nutty (about 5-7 minutes). Add the sliced apples and cook for 3-5 minutes, until the apples soften slightly. Stir in the brown sugar, cinnamon, nutmeg, flour, salt, vanilla extract, and lemon juice. Cook for another 3-5 minutes, until the apples are tender and coated with the syrup. Remove from heat and set aside to cool.
2. Assembling the tarts: Preheat the oven to 375°F (190°C). Roll out the dough on a lightly floured surface to about 1/8 inch thick. Cut out circles large enough to fit into a muffin tin (about 3 inches in diameter). Gently press the dough circles into the muffin tin, making sure the sides and bottoms are covered. Prick the bottoms with a fork a few times to prevent the crust from puffing up. Spoon the cooled apple mixture into each tart shell, filling them generously. Bake for 18-22 minutes, or until the crusts are golden and the apples are tender and bubbling. Let the tarts cool slightly before removing them from the muffin tin.