In a small bowl toss together shallots, 1/4 teaspoon salt, 1/8 teaspoon pepper and 2 tablespoons flour. Set aside.
In a skillet heat 3 tablespoon oil over medium high heat; add shallots and cook until golden and crisp (5 minutes).
Transfer shallots with the oil to baking sheet lined with paper towels.
Wipe out skillet and return to medium high heat, adding remaining oil (2 tablespoons), mushrooms and 1/4 teaspoon salt, cooking stirring until browned (8 - 10 minutes). Transfer to plate and set aside.
Wipe out skillet and heat butter over medium heat, adding onion when butter melts, cooking stirring occasionally until edges brown (2 minutes).
Stir in garlic and remaining flour (1 tablespoon), green beans, thyme and bay leaves.
Stir in cream, broth, increasing heat to medium high, cover and cook until beans are tender (4-5 minutes).
Stir in mushrooms, continuing to cook uncovered until beans are tender and sauce thickens (4-5 minutes). Remove from heat.
Discard bay leaves and thyme, season with salt and pepper.
Transfer to serving dish, sprinkling with reserved shallots.