Cook broccoli as directed on bag until crisp-tender; drain. Set aside 1 1/2 cups of the broccoli.
Place remaining 1 1/2 cups broccoli and all remaining pesto ingredients in food processor. Cover; process until smooth, stopping occasionally to scrape down sides with rubber spatula.
In 4-quart saucepan, cook pasta as directed on package, adding reserved 1 1/2 cups broccoli and bell pepper during last 1 minute of cooking time. Drain; place in serving bowl. Add tomato and pesto; toss to coat. Sprinkle with additional cheese.