Apple and Persimmon Tarte Tatin

Melt butter in 11" skillet over medium heat, brushing sides of skillet with butter as it melts. Sprinkle sugar evenly over bottom of skillet and scrape in vanilla seeds; save pod for another use. Cook, undisturbed, until sugar is evenly moistened, about 1 minute. Stir in salt and 1 Tbsp. brandy, then remove pan from heat.
Arrange as many apples as fit, rounded side down, in a tightly packed circle around outside edge of skillet; reserve remaining apples. Fill in center with persimmons, rounded side down. Cook over medium heat until juices begin to bubble, about 2 minutes. Reduce heat to medium-low and continue cooking (as apples cook, they will shrink; nudge remaining raw apples into gaps, reserving any extra pieces for another use) until apples are tender and caramel is a deep golden color, 35–40 minutes.
Meanwhile, place rack in center of oven; preheat to 400°F. Set skillet on a foil-lined rimmed baking sheet to catch any drips.
Gently roll out puff pastry on a lightly floured work surface and smooth out creases. Cut into a round that will fit snugly and flush inside skillet. Drape puff pastry over apples. Bake until pastry is puffed and golden brown, 30–35 minutes.
Transfer skillet to a wire rack and let stand until bubbling caramel subsides, about 5 minutes. Gently run a butter knife around edges of skillet, then invert a platter with lip over skillet. Using pot holders to hold skillet and platter tightly together, invert tart onto platter. Using a table knife or rubber spatula, press any fruit that sticks to skillet onto tart, then brush any excess caramel in skillet over tart. Let cool at least 15 minutes.
Meanwhile, using an electric mixer on medium-high speed, beat cream to medium peaks in a large bowl, then fold in remaining 1 tsp. brandy. Serve tart with whipped cream.