Into the bowl of a stand mixer, add the warm water and honey. Stir to dissolve the honey.
Sprinkle active dry yeast over the top. Let stand for five minutes, until yeast begins to foam.
Add 1 tablespoon sea salt, 1 tablespoon olive oil, yellow onion, and all-purpose flour.
Using a dough hook attachment, knead the dough for 5 minutes, until smooth and elastic.
Lightly oil a large mixing bowl. Place the kneaded dough into the bowl and turn to coat.
Using a damp cloth (a kitchen towel works great!), cover the bowl.
Set in a warm place and allow the dough to rise for 1 hour, until doubled in size.
Preheat oven to 415 degrees F.
Line a 12-inch x17-inch baking sheet with parchment paper. Punch down the dough then place it on the baking sheet.
Using your very clean hands, press the dough down while pushing out to flatten the dough and cover the surface of the baking sheet.
Using the tip of your finger, make "dimple" indentations spaced about 1-inch apart.
Brush the remaining 2 teaspoons of olive oil over the surface of the dough.
Sprinkle with dried rosemary, parmesan cheese, and remaining 1/2 teaspoon of sea salt.
Let the dough rest for 10 minutes.
Bake in preheated oven for 20 minutes, until golden brown.
Serve warm or room temperature.