Grate the cheese. Chop the dill and parsley. Cut the tomato into small pieces. Slice the onion into half rings.
Heat 2 tbsp vegetable oil in a pan over medium-high heat. Add 200g minced beef and cook for 15 minutes, stirring occasionally, until cooked through. Season with salt and ground black pepper to taste. Transfer to a plate and let cool for 5 minutes.
Lay out the first lavash sheet. Spread roughly 75g grated cheese evenly over the surface.
Distribute half of the cooled minced beef over the cheese.
Top with roughly half of the tomato pieces. Spread 1 tbsp mayonnaise over the tomato.
Add roughly half of the sliced onion. Sprinkle roughly half of the chopped dill and parsley over the onion.
Season the filling lightly with salt and ground black pepper. Roll the lavash tightly from one end to form a cylinder.
Repeat steps 3–7 with the second lavash sheet and remaining filling ingredients to create the second roll.
Heat 4 tbsp butter in a pan over medium-high heat. Place both rolls seam-side down in the pan and fry for 3–4 minutes per side until they develop a golden brown crust.