Preheat the oven to 400°F. Butter a shallow 3-quart casserole. Bring a large pot of salted water to a boil.
Line a plate with paper towels. Place the sliced shallots in a small saucepan and pour in canola or vegetable oil to cover. Place the pan on the stove, turn the heat to medium and allow the shallots to cook, with the heat barely at a simmer, stirring occasionally until they turn medium brown, about 5 minutes. Drain them in a fine-mesh sieve, reserving the oil for another use, then turn the shallots onto the paper-plate lined plate and blot with another paper towel. Sprinkle with salt.
Fill a large bowl with water and some ice. Plunge the haricot verts into the pot of boiling water, and cook for about 5 minutes, just until crisp tender. Drain and plunge the partially cooked green beans into the ice water to stop the cooking. Drain.
Melt the butter in large skillet. Sauté the mushrooms until browned, and any liquid they have released has evaporated, about 6 minutes. Add the chopped shallots and sauté for another 2 minutes until the shallots are slightly softened. Sprinkle over the flour, and continue to sauté for another 2 minutes until the flour coats the mushrooms well, and turns golden. Slowly pour in the broth while stirring. Stir in the half and half, and continue to cook, stirring frequently, until the liquid thickens. Add the partially cooked green beans. Turn into the prepared casserole. Bake until hot and bubbly, about 15 minutes. Sprinkle over the crispy sliced shallots and bake for 2 to 3 more minutes until shallots are hot and re-crisped. Serve hot, with the parsley or chervil if desired.