Add yeast to the bowl of a mixer and add warm water and stir gently to dissolve yeast. Let sit for 3-5 minutes until yeast begins to activate (when it starts to foam).
Meanwhile, add minced garlic to 1/2 cup of olive oil.
With the dough hook attachment mix on low then add flour, salt, and 2 tablespoons of garlic olive oil. Continue to mix until dough comes together then turn to medium and mix until dough is smooth.
Add 2 tablespoons the oil to a large bowl, add the dough and turn in bowl to coat. The cover the bowl with a tea towel and let rise in a warm space for at least 90 minutes or until double in size.
Pre-heat oven to 450 degrees.
Spread a tablespoon of olive oil to a rimmed baking sheet. Uncover the dough, punch it down, and then place the dough on the baking sheet. Stretch the dough out on the baking sheet and then cover to rise for another 30 minutes.
Uncover dough and then with your fingers, dimple with oil greased fingers. With a pastry brush, use the remaining oil to brush the top of the dough and then sprinkle with rosemary and coarse sea salt.
Either use a egg wash or give a water spray.
Turn oven down to 375 and then place the dough in the oven and bake until golden brown (25-30 minutes).
Remove from oven and remove from pan and cool on cooling rack.
Cut and serve with oil and vinegar!