Stir Dry Ingredients: Stir together 1 ½ cup flour, 2 Tbsp white sugar, 1 Tbsp baking powder, and ½ tsp salt in a large bowl.
Stir Wet Ingredients: In a separate bowl whisk 1 ¼ cup milk, 1 large egg, and 1 tsp vanilla extract. In a separate bowl, melt 4 Tbsp butter in the microwave, then drizzle it into the milk mixture while whisking (it will solidify; that's okay).
Combine: Add milk mixture to the flour mixture, stirring until mostly combined (some lumps in the batter is okay, do not over stir). Let rest for about 5 minutes to maximize their fluffiness.
Cook: Lightly grease or butter a large saute pan and set over medium heat. Once hot, spoon in ¼ cup portions of batter, leaving space between each pancake. Cook for 2 to 3 minutes, until bubbles form on the surface, the edges look set, and the underside is golden brown. Flip and cook another 1 to 2 minutes, until the second side is golden and the pancakes spring back when gently pressed. Adjust heat as needed to keep them from browning too quickly.
Serve: Set oven to 200°F (95°C). Keep cooked pancakes warm by setting on a baking sheet and keeping then in the oven while you finish cooking the rest of the pancakes.