To make the shiitake and shallots, preheat the oven to 375ºF and line a baking tray with parchment paper. Place the shiitake and shallots on the baking tray and drizzle with oil. Arrange in a single layer on the tray and sprinkle with salt and pepper. Bake for 20 to 25 minutes or until everything is dark and crispy. Remove from the oven and set aside.

To make the garlic breadcrumbs, place everything in a food processor and pulse until the bread crumbs are coarsely ground and everything is well-combined.

To make the green beans, adjust the oven temperature to 425ºF. Line a baking sheet with paper towels or a clean dishtowel. Lightly oil an 8-inch square baking dish. Bring 4 quarts of water to a boil in a large pot or Dutch oven. Add green beans and 2 tablespoons of salt. Keep water at a gentle boil and cook green beans for about 4 minutes, or until beans are crisp-tender. Drain and transfer beans to the prepared tray. In the same pot, heat oil over medium heat. Add garlic, salt, and pepper. Cook for a minute or two, without browning, until fragrant. Stir in flour and nutritional yeast and cook for another minute. Slowly whisk in broth and bring to a simmer. Stir in milk and cook for a few more minutes until the mixture is smooth and slightly thickened. Taste and season with more salt and pepper, if desired. Stir in yogurt then add green beans and stir until evenly coated with sauce. Transfer to the baking dish and sprinkle with breadcrumbs. Bake for about 15 minutes, until the topping is golden brown and sauce is bubbling around the edges. Remove from the oven and arrange shiitake and shallots evenly on the top. Serve immediately.