Preheat oven to 325°. Butter and generously flour a 9-in. springform pan. Shake out excess flour and set aside.
Using a paring knife or sharp corer, core apples from stem down through seeds and base to remove in one cylinder. Peel apples and slice crosswise into 1/4-in. rings. Set apples aside.
In a large bowl, using a mixer with whisk attachment, beat eggs and granulated sugar on high speed until pale and slightly thickened, 1 1/2 to 2 minutes. Reduce speed to medium and add cream and vanilla. Beat about 30 seconds more to blend. Add flour, baking powder, and salt and blend on low speed until evenly combined.
Add apples (including any uneven end pieces) to batter and stir gently with a spatula to coat, separating slices. Pour mixture into prepared pan and arrange apples flat.
Bake cake until golden brown on top and a toothpick inserted into center of cake (rather than an apple piece) comes out clean, 1 to 1 1/4 hours. Let cake cool on a rack 20 minutes, then run a slender knife between edge of cake and pan. Remove pan rim and cool cake at least 10 minutes more.
Serve warm or at room temperature, dusted with powdered sugar and topped with spoonfuls of crème fraîche if you like.