Trim and cut meat into 1-1/2-inch (4 cm) cubes. In shallow dish, season 2 tbsp (25 mL) flour with salt and pepper; add meat and toss to coat lightly. Set aside. In large nonstick skillet, heat half of the oil over medium heat; cook mushrooms for 3 minutes or until tender. Transfer to bowl along with juices. Add remaining oil to skillet; brown beef in two or three batches, turning to brown all over. Transfer beef to mushrooms.

Stir remaining flour into broth; add to skillet and cook, scraping up brown bits, until thickened.

Grease bottom of a 10-cup (2.5 L) casserole dish; overlap half of the potatoes in dish. Spread with half of the onions. Season with salt and pepper to taste; sprinkle with half of the parsley. Top with meat, then mushrooms and any juices; sprinkle with half of the thyme. Cover with carrots; season with salt and pepper. Sprinkle with remaining parsley and thyme.

Pour in broth mixture. Layer with remaining onions, then potatoes; brush with butter. Cover and bake in 325°F (160°C) oven for 2 hours or until tender throughout. Uncover and bake for 25 to 30 minutes or until lightly golden. To make ahead, let cool for 30 minutes; cover and refrigerate for up to 2 days. Reheat in 325°F (160°C) oven for 35 minutes.