Step 1

Combine shallots and oil in a wok or medium nonstick saucepan. Shallots should barely stick out above level of oil. Place over high heat and cook, stirring frequently, until shallots are completely soft, about 12 minutes.

Step 2

Meanwhile, line a rimmed baking sheet with 6 layers of paper towels. Continue to cook shallots, stirring constantly, until shallots are light golden brown, about 8 minutes.

Step 3

Immediately strain through a fine-mesh strainer set in a heat-proof bowl or saucepan. Set shallot oil aside. You should have about 2 cups of fried shallots.

Step 4

Transfer fried shallots to paper towels. Lift up one end of top paper towel and roll shallots off onto second. Blot with first towel to absorb excess oil. Repeat 4 more times, transferring shallots from one paper towel to the next, until only one paper towel remains. Season well with salt.

Step 5

Allow shallots to cool completely, about 45 minutes. Once they've cooled, transfer to a sealed airtight container. Shallots can be made up to 1 month in advance.

Step 6

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.

Step 7

Combine soy sauce, lemon juice, chicken stock, and heavy cream in a 1-quart liquid measuring cup or medium bowl.

Step 8

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.

Step 9

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.

Step 10

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.

Step 11

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.

Step 12

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.

Step 13

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. Bake until hot and bubbly, 15 to 20 minutes. Top with remaining cup fried shallots and serve.