In a small bowl, gently stir the warm water, yeast, and honey. Let rest in a warm spot until foamy, about 10 minutes. If the yeast doesn’t foam up, discard it and start over.
In the bowl of a stand mixer fitted with the paddle attachment, combine the flour, salt, ¼ cup of the olive oil, and yeast mixture until the dough begins to come together. Switch to the dough hook. Knead the dough on high for 5 to 7 minutes, until it becomes soft and somewhat elastic.
Transfer the dough to a well-floured work surface and knead a few times by hand. Oil a bowl well. Shape the dough into a bowl and place in the bowl, turning over to coat both sides. Cover loosely with plastic wrap and a damp kitchen towel. Let rest in a warm spot until doubled in size, about 1 hour.
Line a baking sheet with parchment paper and drizzle with the remaining 2 tablespoons olive oil. Transfer the dough to the prepared baking sheet and stretch out with your hands to fully cover the baking sheet with dough. Using your fingers, make indentations all across the top. Cover with plastic wrap and a damp kitchen towel and let rest in a warm spot for another hour.
Preheat the oven to 400ºSprinkle the bread evenly over the top with the rosemary and Parmesan. Bake the focaccia until golden brown on top, 20 to 25 minutes. Remove from the oven and let cool down before cutting. Cut into 16 squares and use immediately. Any leftovers can be stored in an airtight container at room temperature for up to 3 days.