In a mixing bowl, combine the farmer's cheese, egg, flour, sugar, vanilla extract, salt, and baking powder. Mix until well combined and a soft dough forms. If the mixture is too wet, add a little more flour until it holds together but remains soft.
Divide the dough into 8 equal portions and shape each portion into a small patty, about 1/2 inch thick.
Heat the vegetable oil in a large skillet over medium heat. Once hot, add the patties to the skillet, making sure not to overcrowd the pan.
Cook for about 3-4 minutes on each side, or until golden brown and cooked through. Adjust the heat as necessary to prevent burning.
Remove the pancakes from the skillet and place them on a paper towel-lined plate to absorb excess oil.
Serve warm, dusted with powdered sugar and accompanied by fresh berries or fruit preserves, if desired.