Whisk warm water with the yeast and sugar in a bowl; let sit for 10 minutes until foamy and activated.

In a stand mixer bowl fitted with a dough hook, combine flour and kosher salt, then pour in the yeast mixture and olive oil. Knead on low for about 6 minutes until smooth and elastic.

Transfer dough to an oiled bowl, cover with plastic wrap, and let rise for 1-2 hours until doubled in size.

Generously oil a 9x13-inch pan. Gently stretch the risen dough into the pan, cover, and let rise another 45-60 minutes until puffy.

Preheat oven to 425–450°F while the dough finishes rising.

Melt butter in a small saucepan over medium, add minced garlic, and sauté for 1-2 minutes until fragrant. Remove from heat and stir in parsley, red pepper flakes (if using), and sea salt.

Using oiled fingers, press deep dimples into the dough. Brush half the garlic-butter mixture over the top, drizzle with olive oil, and sprinkle with flaky sea salt.

Bake for 20-25 minutes in the preheated oven until deeply golden and crisp around the edges.

Remove from oven and immediately brush with remaining garlic butter, then sprinkle with grated Parmesan and extra parsley. Slice and serve warm.