Preheat the oven to 350 F. Generously mist four 3-1/2-inch-diameter ramekins with spray. Place them side by side in an 8 x 8-inch baking pan. Add water to the pan until it reaches halfway to the top of the ramekins.

Use a sturdy whisk or spatula to mix the applesauce, vanilla, egg whites, and brown sugar in a large mixing bowl until well combined. Add the cocoa powder, espresso, and salt. Stir until just combined and no lumps remain. Divide evenly among the ramekins (each ramekin will be about two-thirds full).

Bake for 21 to 24 minutes, until the tops look silky and puff slightly and a toothpick inserted in the center comes out a bit wet. Remove from the oven and carefully transfer the ramekins from the water bath to a cooling rack. Cool for 5 to 10 minutes. Then invert each ramekin onto a dessert plate. Let stand for 1 minute, and then slowly lift off the ramekin (the cakes should come out on their own, but if they don't, run a knife around the edge to loosen them). Cool for another 5 to 10 minutes. Use a fine sieve to evenly dust each cake with a light sprinkling of powdered sugar. Place one raspberry on the center of each cake, if using. Serve immediately.