In a large bowl mix flour, salt, egg, and egg yolk, water, and oil, until the dough starts coming together. Lightly sprinkle the working surface with some flour and transfer the dough. Knead the dough for 5 minutes, until smooth. Wrap it in plastic and let rest for 20 minutes.
Mix the cherries with 1 tablespoon of sugar and corn starch. Set aside.
Divide the dough into 2 equal parts and roll into a large 1/8-inch thick circle. Using a 3-inch round cookie cutter, or a simple glass, cut circles of dough. Repeat with the other half of the dough and scraps.
Place 2 cherries on each round of dough. Gently fold the dough over, forming a pocket around the filling. Pinch the edges of the varenyky to seal.
Bring a pot of water to a rolling boil, add 1 tablespoon of sugar. Drop varenyky into boiling water and stir with a spoon to prevent them from sticking together. Cook for about 5 minutes, when varenyky float, they’re done.
Using a slotted spoon or small mesh strainer, fish the varenyky out and place them in a bowl or on a deep plate. Add a small pat of butter and gently toss to prevent them from sticking to one another. Sprinkle with sugar.