Preheat the oven to 180 °C (350 °F) and line a baking tray with parchment paper.
In a large bowl, mix the grated cheeses and softened butter until evenly combined.
Add the salt and sugar and mix well. In a separate bowl, stir the baking soda into the yogurt, then add it to the cheese mixture.
Gradually add the flour, mixing until a soft dough forms. Knead briefly until smooth and not sticky.
Roll the dough on a lightly floured surface to about 0.5–1 cm (¼–⅓ inch) thickness.
Cut the dough into strips or small rectangles, place them on the tray, brush with mix of beaten egg yolk with a bit of water or milk, and sprinkle sesame seeds on top.
Bake for around 15 minutes, until the solenki are golden brown, then let them cool slightly before serving.