Whisk flour, sugar, baking soda, salt, and cinnamon together in a large bowl.
Mash banana in another bowl. Stir in sourdough starter, sour cream, egg, 2 tablespoons butter, and vanilla extract. Add to the flour mixture and stir until just combined. Mix in milk gradually until batter is pourable but some lumps remain.
Heat a griddle over medium-high heat. Grease lightly with melted butter. Pour 1/4 cup batter onto the griddle for each pancake, keeping them 2 inches apart. Cook until bubbles form and the edges are dry, about 2 1/2 minutes. Flip and cook until browned on the other side, about 1 minute. Repeat with remaining butter and batter.
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