Yield: 8 servings (see notes)
Smash mushrooms under the bottom of a large skillet until broken into 1/4- to 1/2-inch pieces. Roughly chop into pieces approximately 1/8 to 1/4 inch in size. Set aside.
Combine soy sauce, lemon juice, chicken stock, and heavy cream in a 1-quart liquid measuring cup or medium bowl.
Add 2 tablespoons (30ml) reserved shallot oil (save remainder in an airtight container for another use) and butter to a 12-inch nonstick skillet. Heat over high heat until butter is melted and foaming subsides. Add mushrooms to skillet and cook, stirring occasionally, until liquid is evaporated and mushrooms begin to sizzle, 6 to 10 minutes.
Reduce heat to medium-high. Add garlic and cook, stirring constantly, until fragrant, about 30 seconds. Add flour and cook, stirring constantly, until light golden blond, 1 to 2 minutes. Whisking constantly, add stock and cream mixture.
Bring to a boil, reduce to a simmer, and cook until mixture achieves a texture between pancake batter and heavy cream, about 5 minutes. Season to taste with salt and pepper.
Adjust oven rack to lower-middle position and preheat oven to 350°F (180°C). Bring 1 gallon (3.8L) water and 1/4 cup (48g) kosher salt to a boil over high heat. Fill a large bowl with 1 quart ice cubes and 2 quarts (1.9L) water.
Add green beans to water and boil until tender but still bright green, about 5 minutes. Drain through a colander set over the sink and immediately transfer to ice water until completely cooled. Drain green beans and set aside.
Combine green beans, mushroom sauce, and 1 cup fried shallots. Transfer to a 9- by 13-inch rectangular baking dish or a 10- by 14-inch oval baking dish (see notes). Bake until hot and bubbly, 15 to 20 minutes. Top with remaining cup fried shallots and serve.