For the Filling:

1. Place the butter in a small saucepan or skillet and melt over medium heat. Swirling the pan every now and then, cook until the butter is lightly golden brown and smells nutty. Watch it carefully, as it can go from brown to burnt in no time.
2. Transfer the browned butter to a medium mixing bowl to cool slightly.
3. Whisk in the sugar and flour and stir until completely incorporated.
4. Whisk in the salt, cinnamon, vanilla, and egg until everything is combined and smooth. 
5. Place the bowl in the fridge for 10 minutes – we want it to cool completely before proceeding. It will firm up and lighten in color as it cools.

For the Tart:

1. Preheat the oven to 400°F and line a large baking sheet with parchment paper.
2. Lightly dust the pastry with flour and then roll the pastry gently to seal the perforations. Using a paring knife, gently cut a ½-inch border into the pastry, being sure to not cut all the way through. This will create a sort of rim to hold in all the filling and apples.
3. Brush the entire surface with egg wash. This will help the edges brown but will also seal in the center so it doesn’t get too soggy from the filling.
4. Spread the brown butter filling evenly over the pastry, being sure to stay within the border.
5. Arrange the apples on top of the filling, overlapping them decoratively.
6. Sprinkle the apple slices with the sugar and then dot the cold butter evenly over the top.
7. Bake the tart for 30-35 minutes or until the pastry is golden brown around the edges and the apples are tender. Some of the filling is likely to overflow in spots – don’t worry! This is OK. Most of the filling will firm up and bake with the apples.
8. While the tart is baking, whisk together the jam and liqueur in a small saucepan until the jam is melted. Brush the mixture over the entire tart once it comes out of the oven.
9. Cool slightly and serve warm or at room temperature with your favorite ice cream.