Prepare the Dough: In a large mixing bowl, combine warm water, sugar, and yeast. Let it sit for 5 minutes until frothy. Add olive oil, sea salt, and bread flour. Mix until a sticky dough forms.
First Rise: Cover the bowl with a damp cloth and let the dough rise in a warm place for 1 hour, or until doubled in size.
Prepare the Pan: Grease a 9×13-inch metal baking pan with olive oil. Transfer the risen dough into the pan, gently stretching it to fit. Cover and let it rest for another 30 minutes.
Preheat Oven: While the dough is resting, preheat your oven to 450°F (232°C).
Make Garlic Butter: In a small bowl, mix melted butter, olive oil, minced garlic, and minced parsley. Set aside.
Dimple the Dough: Using your fingers, press dimples all over the surface of the dough. Drizzle the garlic butter mixture evenly over the top.
Add Cheese: Sprinkle shredded mozzarella and gruyere evenly over the dough.
Bake: Place the pan in the preheated oven and bake for 25 minutes, or until the focaccia is golden brown and the cheese is bubbly.
Cool and Serve: Remove from oven and let it cool slightly before slicing. Serve warm.