Step 1

Place a rack in middle of oven; preheat to 350°. Toast almonds on a rimmed baking sheet, tossing once, until golden brown, 6–8 minutes. Let cool.

Step 2

Reduce oven temperature to 275°. Peel apples; cut in half. Using a melon baller or teaspoon, scoop out cores.

Step 3

Rub cut sides of lemon all over apples, then place apples cut side down in a 13x9" baking dish. Squeeze lemon halves over and add maple syrup, brandy, vanilla, and salt.

Step 4

Cover tightly with foil and bake until juices are bubbling and apples are tender but still intact (poke through foil with a tester or toothpick to check), 60–80 minutes. Uncover and let cool. Increase oven temperature to 400°.

Step 5

Meanwhile, toss almonds, 1 Tbsp. raw sugar, and 1 Tbsp. flour in a small bowl; set aside.

Step 6

Let puff pastry sit at room temperature about 4 minutes to soften slightly. Roll out on a lightly floured sheet of parchment paper, dusting with more flour as needed to prevent sticking and rotating once or twice, to a 16x12" rectangle. Slide parchment paper with pastry onto a large rimmed baking sheet. Trim around sides to straighten and tidy edges, then cut off a 1" strip from each side (you’ll have 4 strips).

Step 7

Brush around edge of rectangle with egg, then place strips on top, aligning with edges. Trim any overhang from corners. Brush rim you just created with egg and sprinkle with remaining 1 Tbsp. raw sugar. Scatter reserved almond mixture over pastry, staying inside the rim.

Step 8

Gently arrange apples on top of almond mixture; reserve juices left in dish. Chill tart 15 minutes.

Step 9

Bake tart 20 minutes. Reduce oven temperature to 350° and continue to bake until pastry is deep golden brown and puffed, 45–55 minutes.

Step 10

Meanwhile, scrape reserved apple juices into a small saucepan and cook over medium heat, swirling pan often, until syrupy (you should have 2–4 Tbsp.), 6–8 minutes. Remove glaze from heat.

Step 11

Remove tart from oven and brush glaze over apples. Serve warm or room temperature with scoops of ice cream.

Step 12

Do Ahead: Tart can be baked 10 hours ahead. Store loosely wrapped at room temperature. Reheat in a 250° oven if desired.