Sift 1 1/4 cups self-rising flour, 2 tablespoons granulated sugar, and a pinch of baking soda into a large mixing bowl. Whisk to combine.
In a separate bowl, whisk together 1 large egg and 2/3 cup milk. Stir in 2 tablespoons melted unsalted butter until just combined.
Make a well in the center of the dry ingredients and pour in the wet mixture. Stir gently until just combined, leaving a few small lumps.
Heat a nonstick skillet over medium heat and lightly grease with additional melted butter.
Drop about 2 tablespoons of batter per pancake onto the skillet. Cook until bubbles form on the surface and the edges look set, about 2 to 3 minutes.
Flip and cook until the second side is golden brown and cooked through, about 1 to 2 minutes more.
Transfer the cooked pancakes to a plate and keep warm in a low oven (about 200°F) or under foil while you cook the remaining batter.