Combine blackberries and raspberries in a bowl. Fold in maple syrup to give the berries a nice shine. Set aside.
Separate egg yolks and whites into 2 mixing bowls.
Add 2 tablespoons plus 1 teaspoon sugar to the yolks; whisk until dissolved. Mix in vanilla extract, milk, and melted butter. Add 1/4 cup plus 1 tablespoon self-rising flour. Whisk just until flour disappears into the batter.
Add cream of tartar to the egg whites. Whip using a large, clean whisk until stiff peaks form.
Stir 1/3 of the whites gently into the batter using a silicone spatula, until mostly smooth but streaks of white remain. Gently fold in the rest of the whites, scraping the batter over the top and occasionally rotating the bowl as you go, until batter is light yellow and fluffy.
Lightly butter a nonstick pan over medium-low to medium heat. Scoop in desired amount of batter. Cover and cook until bubbles form on the surface and edges start to dry, 2 to 3 minutes. Flip pancakes and continue cooking until bottom is golden brown, 2 to 3 minutes more. Repeat with remaining batter.
Serve pancakes on warm plates and top with the berry mixture.