Olive Oil Dough
Mix yeast, salt, sugar, and olive oil with the water in a 5-quart bowl or lidded, non-airtight food container. Mix in flour (without kneading) using a spoon, food processor with dough attachment, or stand mixer with dough hook. Cover loosely and allow to rest at room temperature until dough rises and collapses or flattens on top (about 2 hours).
After the initial rise, the dough can be used but is handled more easily when cold. Refrigerate in a lidded, non-airtight container and use over the next 12 days.
Twenty minutes before baking, preheat oven to 425°. Place an empty broiler tray on any shelf that won’t interfere with the focaccia. Grease a cookie sheet with olive oil or line with parchment paper or a silicone mat.
Dust the surface of the refrigerated dough with flour. Cut off a 1-pound piece, about the size of a grapefruit. Dust with more flour and quickly shape into a ball stretching the surface of the dough around to the bottom on all four sides, rotating the ball a quarter-turn as you go. Flatten dough into a 1/2- to 3/4-inch-thick round, using your hands or a rolling pin and a minimal amount of flour. Place on prepared cookie sheet.
Saute onion slices in 2 tablespoons of olive oil until softened but not browned. Sparingly place the onions over the surface of the dough, leaving a 1-inch border at the edges. Allow most of the dough’s surface to show through the onions to allow the focaccia to brown well. Sprinkle dough with rosemary, salt, and pepper. Lightly drizzle the remaining 1 teaspoon of olive oil over the focaccia, not covering the whole surface. Allow focaccia to rest and rise for 20 minutes.
After focaccia has rested, place the cookie sheet on a rack near the center of the oven. Pour 1 cup of hot water into the broiler tray and quickly close the oven door. Bake for about 25 minutes, or until crust is medium brown. Be careful not to burn the onions. Cut into wedges and serve warm.