Preheat the oven to 350 degrees Fahrenheit. Fill a large bowl with ice and water for when you’re done blanching the green beans.Bring a large (large!) pot of water to boil, with enough room to add the green beans. Add the green beans and 2 teaspoons of the salt. Boil the green beans for 5 minutes, then drain the beans in a colander and immediately pour them into the bowl of ice water to stop the cooking. Then, drain the beans again in your colander, and set aside to drip-dry while you prepare the rest.Meanwhile, melt the butter in a 12-inch cast iron skillet* set between medium and medium-high heat. Once the butter has melted and is starting to turn golden brown in places, add the shallots and mushrooms. (If using olive oil instead of butter, wait until the oil sizzles when you add a piece of mushroom.)Add the remaining ½ teaspoon salt and about 15 twists of black pepper. Cook, stirring occasionally, until the mushrooms begin to release some liquid and turn brown on the edges, about 4 to 5 minutes.Add the garlic and thyme and cook until fragrant, about 30 seconds, while stirring constantly. Sprinkle the flour over the mixture and stir to combine. Cook for 1 minute, while stirring constantly.Slowly pour in the broth, while using your spoon or spatula to scrape up any browned bits on the bottom of the pan. Bring the mixture to a simmer and cook for 1 minute, then decrease the heat to medium-low. Add the half-and-half and cook until the mixture thickens, stirring occasionally, about 6 to 8 minutes.Remove the skillet from the heat and stir in the drained green beans. Evenly sprinkle the mixture with crushed chips. Bake until the edges are nice and bubbly, about 15 minutes. Serve promptly.