Position a rack in the lower third of the oven and preheat the oven to 350 degrees F. Grease and flour the sides of the cake pan and line the bottom with parchment paper.
Add the sugar, flour, salt and baking powder to a food processor and pulse to blend the ingredients thoroughly. Add the cream and butter or oil and pulse quickly, 8 to 10 times, until ingredients are blended (if you’re using oil, the ingredients will be moist and beginning to clump together but not yet smooth). Add the eggs and vanilla and pulse 5 to 6 times. Scrape the sides of the bowl and pulse 5 to 6 more times, just until the ingredients are blended and smooth – no more.
Scrape the batter into the pan and spread it evenly. Bake for 30 to 35 minutes, until a toothpick inserted in the DSC_1181-copycenter of the cake comes out clean. Set the pan on a rack to cool for about 10 minutes.
Slide a thin knife or a small metal spatula around the edges of the cake to detach it from the pan. Invert the cake onto the rack and peel off the parchment liner. Turn the cake right side up on the rack to cool completely. Once cooled, the cake keeps, wrapped airtight, at room temperature for 3 days, or in the freezer for up to 3 months; bring to room temperature before serving.