Preheat oven to 450 degrees, with rack in lower third lined with a pizza stone or baking sheet. Brush a 9-by-2-inch springform or cake pan with oil.

Heat a large skillet over medium-high. Swirl in oil. Add onion, bell pepper, and broccolini; season with salt and pepper. Reduce heat to medium and cook, stirring occasionally, until onion and pepper soften and broccolini is crisp-tender, 12 to 15 minutes. Add artichokes, garlic, pepper flakes, and oregano; cook 1 minute more. Transfer mixture to a plate; let cool completely.

Turn dough out into prepared pan (do not punch down) and flip once to evenly coat. Starting in center of pan and using both hands, press down and outward with fingertips, working dough until it's evenly distributed along bottom and two-thirds up sides of pan.

Sprinkle half of mozzarella evenly over bottom of dough. Toss vegetables with remaining mozzarella and spread evenly in pan. Dollop small spoonfuls of sauce evenly over vegetables; sprinkle with Parmigiano.

Bake until dough is puffed and golden brown, 35 to 40 minutes. Let cool in pan 15 minutes. Remove from pan and cut into wedges; serve.