CAKE

• 12 tablespoons (1½ sticks) unsalted butter, melted, slightly cooled, divided, plus more, room temperature, for pan
• 1¼ cups all-purpose flour plus more for pan
• 4 firm, tart apples (such as Pink Lady or Braeburn; about 2 lb.), peeled, cored, sliced ½” thick
• 2 tablespoons plus 1 cup plus sugar, divided
• 1 teaspoon baking powder
• ¾ teaspoon kosher salt
• 1 teaspoon finely grated lemon zest
• 3 large eggs

• SALTED CARAMEL SAUCE

  • Bring sugar and ¼ cup water to a boil in a small saucepan over medium-high heat, stirring to dissolve sugar. Boil, swirling pan occasionally and brushing down sides with a wet pastry brush, until mixture turns a deep amber color, 8–10 minutes. Remove from heat and slowly add cream (mixture will bubble vigorously). Return to medium heat and cook, stirring occasionally, until smooth, about 2 minutes. Remove from heat and mix in butter and salt. Pour caramel sauce into a small heatproof jar or bowl; let cool.
  • DO AHEAD: Caramel sauce can be made 5 days ahead. Cover and chill.

  CAKE

  • Place rack in middle of oven and preheat to 350°. Butter and flour cake pan; set aside.
  • Heat 2 Tbsp. melted butter in a large skillet over medium heat. Add apples, sprinkle with 2 Tbsp. sugar, and cook, tossing occasionally, until apples are golden brown, 10–12 minutes. Arrange half of the apples in the bottom of prepared cake pan so most of it is covered (a few gaps are okay).
  • Whisk baking powder, salt, lemon zest, 1¼ cups flour, and remaining 1 cup sugar in a large bowl. Whisk in eggs and remaining 10 Tbsp. melted butter until smooth.
  • Pour half of batter over apples in cake pan, top with remaining apples, then pour remaining batter over. Bake cake until top is golden and a tester inserted into the center comes out clean, 40–50 minutes. Transfer pan to a wire rack and let cake cool slightly; turn out onto rack and let cool.
  • Serve cake with caramel sauce and crème fraîche.
  • DO AHEAD: Cake can be baked 1 day ahead. Keep wrapped tightly at room temperature.