Red onions shine in this easy, yeasted flatbread, where they are strewn across the dough with flaky sea salt.
Preheat oven to 450 degrees, with a pizza stone or baking sheet (or an inverted rimmed baking sheet) on lowest rack.
Sprinkle yeast and sugar over warm water in a large bowl. Let stand until foamy, about 5 minutes. Stir in flour, coarse salt, and oil. Transfer dough to a lightly floured work surface. Knead, dusting hands and surface with more flour as needed, until smooth and elastic, about 5 minutes. Shape into a ball.
Transfer to a large oiled bowl, turning to coat. Cover and let rise in a warm spot until doubled in bulk, about 45 minutes.
Punch down dough and form into a ball, then turn out onto a lightly floured surface. Divide into 2 pieces. Gently stretch each into a rough 16-by-6-inch oval and place on a parchment-lined baking sheet (or an inverted rimmed baking sheet). Divide onion between ovals, leaving a 1-inch border; lightly press into dough. Let rise, 10 minutes. Drizzle with oil and sprinkle with flaky salt.
Transfer ovals on parchment onto preheated pizza stone or baking sheet. Bake until crust is golden and crisp, 15 to 20 minutes. Serve warm.