Sift the cocoa powder, baking soda, and salt together into a large bowl. Add the coffee and corn syrup. Blend with a wire whisk until the mixture is smooth and glossy. Add the applesauce, sugar, and vanilla extract. Whisk until completely blended. Add the flour. Fold in the yogurt with a wooden spoon just until it is incorporated.
Fold the batter into an 8-by-8 inch nonstick baking pan. Bake for about 30 minutes, until the mixture is just beginning to separate from the edges of the pan and is firm to the touch in the centre.
Remove from the oven, place on a rack, and cool completely in the pan, about 2 hours.