Preheat oven to 350ºF (180ºC).
Trim roast and cut into 1-inch (2.5 cm) cubes. In large bowl, whisk together flour and half each of the Italian herb seasoning, salt and pepper; add pork, in batches, and toss to coat. Reserve any leftover flour mixture. In large Dutch oven, heat oil over medium-high heat; brown pork in batches. Transfer to plate.
Drain any fat from pan and reduce heat to medium; cook chopped onions, garlic and remaining Italian herb seasoning, salt and pepper, stirring occasionally, until onions are softened, about 5 minutes.
Stir in pearl onions and reserved flour mixture; cook, stirring occasionally, for 5 minutes. Add stock and bay leaf; bring to boil, scraping up any brown bits from bottom of pan. Return pork and any accumulated juices to pan.
Cover and cook over medium-low heat, or in oven, until pork is tender, about 1 hour. Stir in mushrooms and peas; cook, uncovered, until mushrooms are tender and sauce is slightly thickened, about 15 minutes. Discard bay leaf. (Make-ahead: Let cool for 30 minutes; refrigerate in shallow airtight container until cold. Refrigerate for up to 1 day or freeze for up to 2 weeks and thaw in refrigerator for 48 hours before reheating.)