Combine flour, brown sugar, 2 teaspoons cinnamon, cream of tartar, baking powder, baking soda, and salt in a bowl with a whisk.
Combine buttermilk, egg, butter, and vanilla extract in a small bowl. Beat to break up the egg. Pour into the flour mixture and stir until batter is foamy and just combined.
Whisk white sugar and 1 teaspoon cinnamon together in a small bowl.
Heat a large non-stick griddle over medium-low heat. Pour 1/3 cup batter onto the griddle and cook until bubbles form and the edges are dry, 3 to 4 minutes. Flip and cook until browned on the other side, 2 to 3 minutes. Repeat with remaining batter.
Brush pancakes with the 5 tablespoons butter. Sprinkle each with 1 teaspoon of the cinnamon-sugar mixture. Top with whipped cream.