Preheat the oven to 200° C (390°F). Line a large baking sheet with parchment paper.
Place the softened butter and sugar in a large mixing bowl. Using a handheld electric mixer, beat the mixture until pale and fluffy. Trickle in the beaten egg and one tablespoon at a time add the sour cream and beat until fully combined.
In a separate bowl, mix the flour, baking powder and salt.
Add the dry ingredients to the wet ingredients and mix into a soft dough. Do not knead too much, as it won't be soft and tender. Wrap the dough in plastic wrap and place it in the fridge whilst you make the filling. Note that the dough will be quite soft and flimsy, but don't be tempted to add more flour.
Place the farmer's cheese in a large mixing bowl and, using a potato masher or a fork, mash it into a smooth paste (it will still be a little grainy). Add the egg, sugar and flour and mix until everything is well combined. The consistency of your filling won't be too thick. It will spread a little when spooned on the pastry, but shoudn't spill over the edges of the pastry.
Roll the pastry out into a large circle about ½ cm (⅕ in) in thickness. Using cookie cutters, or a small plate, cut out 10-12 x 10 cm (4in) rounds of pastry.
Divide the farmer's cheese filling by spooning it on one half of each pastry disk. Fold the over half of the pastry over, but don't press it down too much (you don't need to seal the filling in). Place the pastries on a baking sheet lined with parchment paper.
Brush the tops of each pastry with a lightly beaten egg yolk.
Bake Grietinieciai in the preheated oven for about 18-20 minutes.