In a small saucepan, bring to a gentle boil 1 cup of milk (reserve the remaining 1/2 cup for later use).
Combine matzo meal, sugar, and salt in a small bowl.
Pour the boiling milk over the mixture. Stir and set aside for 5 minutes (the mixture will thicken).
Mix in the eggs, vanilla, and oil. It may be difficult to mix at first because the mixture is thick, but after a minute of stirring with a whisk, it will become uniform without lumps.
Add the remaining 1/2 cup of cold milk and baking powder to the mixture. Whisk until the batter is smooth and well combined.
Heat a frying pan over medium heat and lightly grease it with butter or oil. Pour the pancake batter using a ladle or a measuring cup with a spout. Tilt the frying pan slightly in one direction as you pour the batter to help spread it thinly and evenly across the surface of the pan. The batter is thin and will spread rapidly.
Cook the pancakes for about 2-3 minutes on one side. Wait until bubbles form on the surface. Then, carefully flip them over and cook the other side until golden brown.
Transfer the cooked pancakes to a plate and cover them with a clean towel to keep them warm.