Mix the topping: Stir 1 tbsp sugar with 1/4 tsp cinnamon in a small bowl; set aside.
Melt 1 1/2 tbsp butter in a microwave-safe mug. Swirl to coat and cool 30 seconds.
Whisk in milk and vanilla until combined.
Add flour, 1.75 tbsp sugar, brown sugar, 1/2 tsp cinnamon, salt, baking soda, and cream of tartar. Stir until smooth.
Smooth the top. Sprinkle cinnamon-sugar over batter. Drizzle 1/2 tsp melted butter, then swirl lightly.
Microwave on High 70–90 seconds until the center springs back but stays moist. Do not overcook.
Rest 1 minute before eating. Enjoy warm straight from the mug.