What's known by pastry chefs as beurre noisette (literally, hazelnut butter) is what makes this Brown Butter Apple Tart so delicious.
Place pie crust in tart pan. Prick bottom and sides and bake as directed. Let cool.
Adjust oven temperature to 350 degrees. Whisk eggs and sugar in a medium bowl just to blend. In a medium saucepan over low heat, cook butter until golden brown, being careful not to burn. Let butter cool for 10 minutes. Slowly whisk brown butter into egg mixture; add vanilla, flour, and salt. Line tart shell with apples. Pour filling over apples.
Bake until apples are deep golden brown and filling is puffed and set in center. Let cool on a wire rack about 2 hours. Serve warm or at room temperature.