Make dough: In bowl of a stand mixer, blend 4 cups flour and the yeast on low speed. Blend in 1 1/2 cups very warm water (120° to 130°) just until dough is evenly moistened, 1 to 2 minutes. Cover with plastic wrap and let rise in a warm place (about 85°) until dough rises slightly and a few bubbles form, 2 hours.
Add salt and 6 tbsp. oil. Using dough hook, mix on low speed until oil is blended in, 3 minutes. Mix on medium speed until no oil is visible, 2 to 5 minutes.
Sprinkle a work surface with flour, put dough on top, and sprinkle with flour. Stretch dough so it's about twice as big, then fold it over onto itself. Give dough a quarter turn. Repeat stretching, folding, and turning three more times. Shape dough into a ball and return, seam down, to bowl. Cover; let rise in a warm place until dough is half again as big, 1 hour.
Stretch, fold, and turn dough four more times; let rise, covered, in a warm place until doubled in volume, 1 more hour.
Pour 3 tbsp. oil into a 12-in. ovenproof frying pan. Gently stretch and fold dough once or twice, form a loose ball, and place seam down in pan. Drizzle with 1 tbsp. oil. Cover with plastic wrap and let rise in a warm place until dough can be easily stretched to edge of pan, 45 to 60 minutes.
Meanwhile, preheat oven to 425° and make toppings: Cook chiles in 1 tbsp. oil in a medium frying pan over medium-high heat until sizzling, 1 minute; set pan aside to cool. Add onion, zucchini, and 1/8 tsp. each salt and pepper to chiles and oil; toss. Firmly push fingers down into risen dough all over to deeply dimple surface and fill pan. Evenly space 1-tbsp. spoonfuls of ricotta on dough and push down into dough. Arrange vegetables over dough. Sprinkle with oil from pan, rosemary, and remaining 1/8 tsp. each salt and pepper.
Bake focaccia until deep golden brown, 35 to 45 minutes. Drizzle with remaining 1 tbsp. oil. Let cool at least 20 minutes, then cut into wedges.
Make ahead: Through step 3, up to 1 day; punch air from risen dough, then chill. Next day, stretch and fold cold dough once, return to bowl, and let stand 2 hours at room temperature before continuing with step Or bake bread 1 day ahead and reheat, draped with foil, in a 350° oven until slightly warm.