In large pot , heat the oil over medium heat. Add the mushrooms and cook for about 5 minutes, or until most of their juices have been released.
Add the onions, broccoli, and peas, and cook for 4-5 minutes, or until onions are semi-translucent.
Add the garlic, rosemary, thyme, pepper, tomato paste, and soy sauce, and cook for 2-3 more minutes, until the herbs are fragrant.
Add the flour and stir until fully incorporated and stir once.
Add the vegetable broth, and bay leaves, and bring to a boil. Reduce the heat to medium-low and simmer for 45 minutes, stirring occasionally, until the stew has thickened.
Remove the bay leaves.