In a small bowl, combine the yeast with half of the warmed water (heated to 110°F) and set it aside for 5 minutes until it becomes foamy.
In a large bowl, place the thinly sliced butter, sugar, and salt.
Pour the remaining warm water into the butter mixture and allow it to sit while the yeast activates.
After 5 minutes, whisk the butter mixture until somewhat combined.
Add the egg yolk and yeast mixture to the bowl, then stir in the flour until just incorporated.
Prepare a 9x13 baking dish by brushing it with 2 tablespoons of melted butter.
Spread the dough evenly in the dish, cover it with plastic wrap, and let it rest for 15 minutes.
Preheat the oven to 350°F.
Remove the plastic wrap from the dough, brush the top with the remaining melted butter, and generously sprinkle with mozzarella, parmesan, garlic salt, and oregano.
Bake for 28-31 minutes, until the edges are deep golden brown and the cheese is bubbly.
Allow the breadsticks to cool for 10 minutes before cutting into 8 even pieces.
Serve warm with marinara sauce for dipping.