Slowly add the egg, lemon zest and vanilla and mix on low speed until smooth. Stop the mixer and add the flour, baking powder and salt, then mix on low speed just until almost combined.
Transfer the batter to a buttered 9" x 9" baking dish, using an offset spatula to spread evenly. Sprinkle about 2 tablespoons of coarse sugar over the cake batter just before baking.