Preheat the oven to 200C/180C Fan/Gas 6.
Toss the apple slices in the brown sugar and lemon juice.
Put the butter in a pan and heat, until brown and nutty. Pour into a cold jug and set aside.
Blitz the caster sugar, eggs and flour in a food processor and slowly add the brown butter and vanilla.
Arrange the apple slices over the base of the pastry case in concentric circles, overlapping them as you go. Scatter over the pecans and pour over the brown butter and egg mixture. Bake the tart for 45 minutes, until golden-brown.
Meanwhile, to make the calvados caramel, heat the sugar over a low heat until melted. Remove from the heat, then stir in the calvados and cream. Place over a low heat to warm.
To serve, cut the tart into slices and serve with the caramel and clotted cream.