Combine yeast, warm water and sugar in large mixing bowl. Mix together and let stand until foamy, 10 minutes.
Add 1/2 C olive oil (reserve the rest for oiling the baking sheet) and all of the rest of the ingredients. Stir to combine until mixture comes into a shaggy ball.
Turn out and knead by hand for 6-8 minutes, or alternatively, mix in stand mixer fitted with dough hook for 5-7 minutes until smooth and elastic.
Cover bowl tightly with plastic wrap and place in a warm area. Allow dough to rise until double (45 minutes). Punch dough down and let rest 5 minutes.
Add remaining 1/4 C olive oil to half sheet pan (15x11x1 inch pan), spread evenly. Turn rested dough out into the greased half sheet pan, pressing into an even layer.
Press fingertips through the dough to create small holes all over dough.
Spray dough with nonstick spray and cover with plastic wrap. Set in warm area to rise until double again, 30-45 minutes. In the meantime, preheat oven to 425 degrees F.
When dough is puffy, remove plastic wrap carefully so dough doesn’t stick(this is why the nonstick spray trick is important). Drizzle 2 TBSP olive oil over dough, press fingers down through dough again, taking special care to press into puffy areas.
Sprinkle coarse salt/sea salt over the olive oil. Place loaf into preheated 425 degree F oven and bake for 25 minutes or until golden brown and hollow sounding when tapped.
Remove from oven and place on a wire rack to cool to warm. Serve warm or at room temperature.
Store leftovers in airtight container, once completely cool.