Step 1

Preheat oven to 425°. Cook 6 Tbsp. butter in a small saucepan over medium heat, swirling often, until bubbling and golden, about 5 minutes; set aside.

Step 2

Prepare your apples: Using a vegetable peeler, remove peel from apples. Stand them upright and slice down along core, working all the way around to remove big lobes of flesh. Cut lobes lengthwise into 1" pieces (irregular shapes are fine). Discard peel and cores. Transfer apples to a large bowl.

Step 3

Add ⅔ cup dark brown sugar, 3 Tbsp. flour, 1 Tbsp. vanilla, 2 tsp. cinnamon, and ½ tsp. salt to bowl with apples.

Step 4

Using a microplane or fine rasp grater, grate zest of ½ lemon over apples. Cut lemon in half and squeeze juice from zested half over apples, catching any seeds. Using peeler, remove peel from ginger, then grate over apples.

Step 5

Toss apple mixture until combined, then transfer to a shallow 3-qt. baking dish. Drizzle all but 2 Tbsp. brown butter over apples.

Step 6

Dust cutting board with a light coating of flour and unfold puff pastry on floured surface. Dust top with flour. Cut puff pastry into irregular 1" pieces (any shape is fine).

Step 7

Arrange pieces of puff pastry over apples, overlapping but spreading to cover almost completely. Brush pastry with remaining brown butter. Sprinkle with granulated sugar.

Step 8

Bake pandowdy until pastry is puffed and golden around edges, 25–30 minutes. Reduce oven temperature to 350° and continue to bake until juices are thick and bubbling and pastry is brown all over, 30–35 minutes longer.

Step 9

Using a spoon, press pastry down into warm juices (but don’t submerge); let cool slightly.

Step 10

Serve pandowdy warm with ice cream.

Step 11

Do Ahead: Pandowdy can be made 1 day ahead. Let cool. Cover loosely with foil and store at room temperature. Reheat uncovered in a 200° oven 20 minutes before serving.