Step 1: Melt the butter in a light-colored saucepan over medium heat until it foams, browns, and smells nutty. Pour into a bowl and let it cool completely.
Step 2: In a large bowl, whisk together flour, granulated sugar, and salt.
Step 3: Incorporate half of the cooled brown butter into the flour mixture using a pastry cutter until it resembles coarse crumbs.
Step 4: Add ice water one tablespoon at a time until the dough just comes together. Wrap in plastic and chill for 30 minutes.
Step 5: Preheat your oven to 375°F (190°C) and grease 8 tartlet tins.
Step 6: Roll out the dough and cut circles to fit the tins. Press the dough into the tins and prick the bottoms with a fork.
Step 7: In a separate bowl, toss sliced apples with brown sugar, cinnamon, nutmeg, lemon juice, vanilla, and the remaining brown butter.
Step 8: Arrange apple slices in a spiral pattern inside the tartlet shells.
Step 9: Bake for 30-35 minutes or until the pastry is golden brown and the apples are tender.
Step 10: Allow to cool slightly before removing from tins and serving.