Whisk together the flour, baking powder, and salt in a bowl.
In a separate bowl, whisk together the milk, egg, melted butter, sugar, and vanilla extract.
Pour the bowl of wet ingredients into the bowl of dry ingredients and stir just until combined. The mixture should be thick, but still pourable, and a little bit lumpy. Let the batter rest for 15 minutes.
Heat a large skillet or griddle over medium. Once hot add enough cooking oil to coat the surface (I use about ½ tsp per pancake). Add the pancake batter to the hot griddle, ¼ cup at a time. Use the back of the measuring cup to spread the batter into a 4.5-inch diameter circle.
Cook the pancakes until bubbles form over the surface and begin to pop, the edges of the pancakes look dry, and the bottom is golden brown (about 60 seconds). Flip the pancakes and cook on the second side until golden brown (about 30 seconds).
Repeat with the remaining batter, adding more oil to the skillet between batches or as needed, until all of the pancakes have been cooked. Keep the pancakes warm on a plate under a towel or in a warm oven until all of the pancakes have been cooked. Serve warm with your favorite toppings!
*¾ cup of milk makes a super thick batter, but aslightly dry pancake. One cup of milk makes a thinner batter and pancakes that are not quite as thick and fluffy. ¾ cup plus 2 Tbsp milk made perfectly thick and fluffy pancakes. You can adjust the milk to make the batter the consistency that you prefer. Using slightly warm milk helps the butter stay melted, which allows it to incorporate evenly into the batter.