Fill a big pot with water (at least 6 quarts), cover, and set on the stove over high heat.

While that comes to a boil, pan-fry the shallots: Find the largest skillet you have (mine is 12 inches in diameter) and add enough vegetable oil to create a thin (figure about ¼-inch) layer coating the bottom. Add the shallots in an even layer, then set on the stove over high heat. When the shallots start hissing and bubbling, lower the heat to medium. Cook until deeply golden brown—lowering the heat and stirring as needed to ensure even cooking—about 15 minutes. Remove to a paper towel–lined surface to cool. Season with a pinch of salt.

Discard the oil and wipe out the skillet to remove any excess. Add the butter and set on the stove over medium-high heat. When the butter has melted, add the mushrooms. Season with a big pinch of salt. Use tongs or a wooden spoon to toss the mushrooms, making sure they’re evenly coated. Cook, stirring once or twice, for about 10 minutes—until all the mushroom-y liquid is gone and they’re beginning to brown and stick to the bottom of the pan.

Pour the cream into the pan with the mushrooms. Add 1 teaspoon salt plus the black pepper, and stir to combine. Bring to a boil. Continue to boil, stirring frequently to prevent burning, for about 13 minutes, slowly reducing the heat toward the end. By the end, the sauce should be chestnut-y in hue, intensely flavored, and so thick that if you drag a wooden spatula or spoon across the bottom of the pan, it leaves a distinct trail for a couple seconds, like with a thick gravy.

While the cream is reducing, cook the green beans: Add 6 tablespoons salt to the boiling water. Now add the green beans. Cook for 3 ½ minutes until bright green and just tender. Drain immediately and spread out on a towel to dry as much as possible. You don’t want them at all wet when they go into the cream sauce.

When the mushroom sauce is as thick as you want it, cut the heat and season with salt to taste. Add the green beans and toss to coat completely. Top with the crispy shallots and serve.