Combine the dry ingredients. In a medium bowl, whisk together the flour, sugar, baking powder, baking soda and salt.
Combine the wet ingredients. In a large bowl, whisk together the Greek yogurt, 1 cup milk, egg, melted butter and vanilla extract until mostly smooth.
Make the batter. Gradually add the dry ingredients to the wet ingredients, stirring just until combined. Add more milk, a few tablespoons at a time, until the batter is thick but pourable. You may need up to 1 1/2 cups milk total. A few small lumps are perfectly fine.
Let the batter rest. Allow the batter to rest for 5 minutes. It should pour easily from a measuring cup and slowly spread after hitting the skillet. If it becomes too thick while resting, stir in an additional splash of milk.
Preheat the skillet. Heat a large skillet or griddle over medium-low to medium heat. If using an electric griddle, set it to approximately 350°F. Lightly coat the cooking surface with butter or cooking spray.
Cook the pancakes. Pour 1/3-cup portions of batter onto the hot skillet. If necessary, use the back of the measuring cup to gently guide the batter into circles.
Flip the pancakes. Cook for 2 to 3 minutes, until bubbles appear on the surface and the edges look set. Flip and cook for another 1 to 2 minutes, until the second side is golden brown and the centers are cooked through.
Repeat and serve. Lightly grease the skillet between batches as needed. Serve the pancakes warm with butter, maple syrup and your favorite toppings.