Preheat the oven to 400°F. Place a large sheet of parchment paper over a baking sheet. Unroll your puff pastry sheet (or if you've made your own, roll it out on a lightly floured surface to 10 1/2" by 15 1/2”). Use a fork to pierce all over the puff pastry.
In a large bowl, very gently toss the apple slices with the lemon juice and brown sugar. Layer the apple slices on the puff pastry square however you prefer, diagonally or straight down. Just make sure you slightly overlap the apple slices.
Bake the tart for approximately 40 minutes, until the edges of the apples and puff pastry begin to brown. The apple juices that stream off the tart will burn quickly on the parchment paper - do not worry, this is OK.
Immediately loosen the tart from the pan using a metal spatula. Transfer the tart to your serving plate. Warm up the fig preserves in the microwave for about 30 seconds. Use a pastry brush to brush the fig preserves all over the tart. Enjoy warm or room temperature.