Mix the warm water, yeast, and honey in a bowl and let sit for 10 minutes to activate.
Add the gluten free all-purpose flour, salt, and half of the extra virgin olive oil to the yeast mixture. Beat until a smooth, thick batter forms.
Pour the remaining olive oil into a 9x13 inch baking pan, spreading it evenly. Transfer the batter into the pan, using oiled hands to press it out to the edges.
Cover the pan and let the dough rise in a warm spot for 45 minutes, or until noticeably puffy.
Preheat the oven to 400F. Use your fingers to press deep dimples all over the surface of the dough.
Sprinkle the fresh rosemary and coarse sea salt evenly over the top.
Bake for 25 to 30 minutes until the top is deeply golden brown and crispy.