In a large bowl, add your flour, sugar, salt, and yeast. In a second bowl warm the water, then add the room-temperature egg yolk and butter. Stir, butter should be mostly melted at this point.
Combine wet and dry ingredients. Stir it all together until just combined. I use the end of a wooden spoon.
Grease the dish with some oil. Dump the dough into a glass baking dish (I used an 8x8 square one). Shape and push dough (slightly kneading if needed) into the dish to form a square. Cover with plastic wrap or clean tea towel.
Let rise in a warm spot for 15-30 minutes.
Preheat oven to 350F. Remove the plastic wrap from the baking dish. Drizzle the remaining melted butter or oil over the top, using a brush to spread it evenly across the dough until fully coated.
Add freshly shredded mozzarella, seasonings, and parmesan.
Bake for 28-31 minutes, or until the edges around the baking dish are a deep golden brown and the cheese on top is bubbly and nicely browned. Remove the pan from the oven and let it cool for about 10 minutes.
Then, lift the breadsticks out of the pan and slice them into even pieces. Serve warm with marinara sauce for dipping.