Pour the 2 cups of warm water into a medium mixing bowl. Add the active dry yeast and granulated sugar, then whisk until thoroughly combined.

Leave the mixture undisturbed for 10 minutes. A layer of foam should develop across the surface, indicating that the yeast has activated.

Add the all-purpose flour and kosher salt to the bowl of a stand mixer fitted with a dough hook. Briefly whisk the dry ingredients together to distribute the salt evenly.

Pour the activated yeast mixture into the flour mixture. Knead on low speed for 6 minutes, or until the dough becomes elastic and begins pulling cleanly away from the sides of the bowl.

If kneading without a stand mixer, work the dough by hand until it develops a smooth, stretchy, and elastic texture.

Lightly coat the inside of a large bowl with extra-virgin olive oil. Transfer the kneaded dough to the prepared bowl and turn it so the exterior is lightly covered with oil.

Seal the bowl securely with plastic wrap and refrigerate for 24 hours. This extended cold fermentation develops the focaccia's flavor and contributes to its airy texture.

Remove the refrigerated dough. Pour 1/4 cup extra-virgin olive oil into a 9 × 13-inch metal baking or cake pan, spreading it evenly over the base.

Set the chilled dough in the oiled pan and gently stretch it toward the edges. Cover the pan and allow the dough to rest at room temperature for 15 minutes.

Once rested, the dough should be easier to handle. Using your fingertips, carefully extend it until it reaches the edges of the pan.

Cover the pan tightly once more and leave the dough to rise at room temperature for 3 hours.

Preheat the oven to 450°F. Once the oven reaches temperature, allow it to remain heated for an additional 5–10 minutes so the interior is thoroughly hot.

Remove the covering from the risen dough. Drizzle approximately 2 tablespoons of olive oil over the surface, then press your fingertips deeply into the dough to form characteristic focaccia dimples throughout.

Scatter several pinches of flaky sea salt over the top.

Bake for 20–25 minutes, until both the surface and sides are richly golden brown. Rotate the pan halfway through the baking period to encourage even coloring.

While the focaccia bakes, melt the salted butter in a small saucepan or skillet over medium to medium-low heat.

Stir in the minced or pressed garlic and cook for approximately 1 minute, just until fragrant and beginning to develop a light golden color.

Immediately remove the pan from the heat and pour the garlic butter into a heatproof bowl so the garlic does not continue cooking and burn.

As soon as the focaccia comes out of the oven, pour the warm garlic butter evenly across the surface. Use a pastry brush to distribute the butter and garlic over the entire top.

Scatter chopped flat-leaf parsley over the bread, then generously finish with freshly grated Parmigiano Reggiano.

Allow the focaccia to cool slightly on a wire rack to help preserve its crisp exterior, or slice and serve while it remains warm.