This French apple cake is soft, perfectly sweet, and packed with all the fall flavors you love. A comforting dessert that no one will guess is gluten-free!
Preheat the oven to 350°F (175°C) and place a rack in the center. Grease a 9-inch (23-cm) springform or regular cake pan with butter or nonstick spray. If using a regular pan, also line the bottom with parchment paper and grease it once more.
In a small bowl, whisk together the flour, baking powder, and salt. Set aside.
In a mixer, beat the butter and sugar until light and fluffy (about 3 minutes).
Add the eggs one at a time, beating well after each. Mix in the vanilla and rum.
Add the flour mixture and mix on low speed until just combined.
Fold in the chopped apples with a spatula.
Pour the batter into the prepared pan and smooth the top. Sprinkle with brown sugar.
Bake at 350°F (175°C) for about 45–50 minutes, until golden and a toothpick comes out clean.
Cool in the pan on a rack. Run a knife around the edges.
If using a springform pan, remove the sides. If using a regular pan, invert onto a rack, remove the parchment, then flip onto a serving plate.
Dust with powdered sugar if desired. Serve warm or at room temperature, plain or with whipped cream or ice cream.