Stir milk, orange juice, and orange zest together in a bowl. Mix flour, sugar, baking powder, baking soda, and salt together in a separate large bowl. Whisk egg, butter, and vanilla extract into the orange juice mixture. Whisk orange juice mixture into flour mixture until smooth batter forms.
Heat a lightly oiled skillet over medium-high heat. Drop batter in 1/4-cup spoonfuls 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.
