To a small container, add lukewarmwater, instant dry yeast, and sugar. Stir and set aside for one minute.
To a large mixing bowl, add flour and salt. Stir to combine.Add the yeast-water mixture, oliveoil, and mix with a wooden spoon till you have a wet and sticky dough (about 2 minutes).
PROOFING (pick one method)
QUICK PROOFING: cover bowl with damp cloth, leaving enough space between the dough and the cloth.Proof in a slightly warm oven for 1½ to 2 hours, or until double in volume.SLOW PROOFING: cover bowl with plastic wrap and put in the fridge between 8 to 36 hours, then take out of the fridge and let sit at room temperature for 1 hour.
FOLDING AND SECOND PROOFING
After proofing, fold the dough on itself 40 times from the outside to the inside, in the bowl, with a spoon or spatula (it takes 1 minute). See video for technique.
Grease baking pan with 1½ tablespoons of olive oil or line it with parchment paper if you want to avoid oil. Transfer the dough in the pan.
Spread dough on the tray with the back of two spoons dipped in water. The dough is elastic and will pull back, so don't worry if you can't cover the whole tray.
Proof a second time in a slightly warm oven for 45 minutes to 1 hour without covering it.Take the focaccia out of the oven and preheat the oven to 450°F or 230°C.
TOPPING
While the oven warms up, mix extra virgin olive oil, water, and salt in a small bowl.Dip your fingers in the oil-water mixture, then sink them in the dough making dimples across the focaccia.Pour the remaining oil-water mixture all over the focaccia, allowing the liquid to go into the crevices.
Top with fresh rosemary and sprinkle with coarse sea salt or flaky sea salt. Regular salt works, too, if you don't have those fancier salts.
BAKE THE FOCACCIA
When the oven is hot, bake the focaccia on the medium-low rack for 18 to 25 minutes, or until golden and crisp on top and on the bottom.
Let cool down 5 minutes before removing it from the pan and cutting it into squares with a bread knife.