In a small bowl, stir together water, yeast and sugar, then cover and place in a warm area to activate the yeast (about 20 minutes).
When the mixture is nice and bubbly, add it to the bowl of a stand-up mixer (fitted with a dough hook), along with flour, 1 Tb. Kosher salt, and 1/2 c. olive oil. Start the mixer on low until it's combined, and gradually work up to medium speed, for a total of 5-6 minutes.
Remove dough from bowl and place on a floured surface; knead it a few times.
Coat a large glass bowl with olive oil. Place dough in bowl, cover with plastic wrap, and let sit in a warm area for about 1 hour so it doubles in size.
Pour the remaining 1/2 c. olive oil into a 12X17 rimmed baking sheet.
Remove dough from bowl and place onto the oiled baking sheet. Flip it over so all sides are covered in oil. Press the dough toward the outer edges of the sheet, digging your fingers into the dough to form indentations (don't worry if you make holes in the bottom of the dough - it's all good). Place the sheet in a warm place to let it rise again for about 1 hour.
Preheat oven to 425 degrees.
Carefully place toppings onto the dough, pressing gently to secure them. Sprinkle with a little more olive oil and the flaky salt. Bake for 25-30 minutes, until nicely browned (careful not to burn your toppings).
Remove from oven and allow to cool for a few minutes before serving. It's best served warm!