How to Make It
Preheat the oven to 350° and butter and flour a 9-inch round cake pan. In a medium bowl, whisk the flour with the baking powder and salt. In a large bowl, using a handheld electric mixer, beat the butter at medium speed until creamy. Add both sugars and beat until fluffy. Add the eggs one at a time, beating well between additions, then add the crème fraîche and vanilla. At medium-low speed, beat in the dry ingredients until smooth and evenly combined.
Scrape the batter into the prepared pan and smooth the surface. Bake in the center of the oven for about 1 hour, until the cake is golden and springy and a toothpick inserted into the center comes out with a few moist crumbs attached. Let the cake cool in the pan for 20 minutes. Turn the cake onto a plate then invert onto a rack and let cool.
Poke the top of the cake all over with a skewer and pour the caramel sauce over the cake, allowing it to seep in and drip down the side. Cut into wedges and serve.
The unglazed cake can be stored at room temperature for up to 3 days.
Vanilla paste is available at specialty food shops.