In a small bowl, combine the yeast with 2 tablespoons of warm water. Let it sit until foamy, about 5–10 minutes.
In a large mixing bowl, combine the yeast mixture with the remaining warm water, sugar, salt, butter slices, egg yolk, and flour. Stir until a dough forms.
Flour your work surface and knead the dough for 5–7 minutes until smooth and elastic.
Place the kneaded dough into a greased bowl, cover it up, and let it rise for 1–2 hours or until it doubles in size.
While the dough rises, preheat your oven to 400°F (200°C) and prepare a baking sheet with parchment paper.
Once risen, roll the dough into a rectangle about 1/2-inch thick. Brush with half of the melted butter.
Evenly sprinkle the shredded mozzarella over the dough. Fold it over to enclose the cheese and press the edges to seal.
Slice the dough into sticks and arrange on the baking sheet. Brush the tops with the remaining melted butter, and sprinkle with parmesan, garlic salt, and oregano.
Bake for 12–15 minutes, or until golden brown and the cheese is melted.