In a small bowl, dissolve the yeast in half of the warmed water and let it sit until foamy.
In a separate large bowl, place the butter, sugar, and salt.
Pour the remaining warm water over the butter mixture and let it sit.
After five minutes, whisk the butter mixture to combine, even if the butter hasn’t fully melted.
Add the egg yolk and proofed yeast mixture, whisking to incorporate.
Stir in the flour until just mixed.
Grease the baking dish with melted butter, ensuring the bottom and sides are coated.
Spread the dough evenly into the pan, cover with plastic wrap, and let it rest for 15 minutes.
Preheat the oven to 350°F.
Uncover the dough and brush the remaining melted butter over the top.
Sprinkle mozzarella, parmesan, garlic salt, and oregano evenly across the surface.
Bake for 28-31 minutes, until the edges turn dark golden brown and the cheese is bubbly and slightly browned.
Remove from the oven and allow the breadsticks to cool for 10 minutes.
Carefully lift them from the pan and cut into 8 even slices.
Serve warm with marinara sauce for dipping.