Meanwhile, prepare your onions: Heat a large sauté pan over medium heat. Once hot, add 2 tablespoons olive oil. Once the oil is heated, add the onions and 1 teaspoon kosher salt. Cook onions, stirring every minute or two, until a medium brown, almost caramel colored, about 25 minutes. [See Note at end.] Scrape onions onto a plate to cool while you finish the bread.
Finish the focaccia: When the dough is doubled, pour 2 tablespoons olive oil into a 9×13 cake pan. Do not deflate your dough, just scrape it into the oiled pan. Drizzle the top of the dough with another tablespoon of olive oil and use your fingers to dimple the dough, flattening it out. It’s okay if it doesn’t reach the edges. Let the dimpled dough rest at room temperature for 15 minutes and heat your oven to 425°F. After 15 minutes, dimple the dough only where needed a little further into the corners. Let rest for a final 15 minutes before scattering the top with onions, poppy seeds, and a few pinches of salt.
Bake the focaccia: For 25 minutes, until deeply golden brown at the edges and across the top. While it bakes, you can prepare any toppings you’d like to serve it with, such as cream cheese or butter, lox, thinly sliced tomatoes, cucumbers, onions, or capers.
To serve: Loosen the focaccia if it’s stuck in any place and slide it into a cutting board. Cut into 12 squares, using a sharp knife to get through the onions on top without pulling them off, and replacing any that scatter. Eat right away.
Do ahead: Focaccia keeps at room temperature for 1 to 2 days. Reheat on a baking sheet at 350°F for 10 to 12 minutes.
Note: These are not caramelized onions; we do not need 60 to 90 minutes over low heat with constant stirring. That is not how any ancestor of mine cooked onions. I’m intentionally using a higher heat for more quickly developed flavor. If they’re not picking up color by 20 minutes, bump up the heat slightly. If they’re coloring too fast to make it to 20 to 25 minutes, reduce the heat. We want to stopping shy of a dark bronzed color, as the onions will finish in the oven and we don’t want them to burn.