Combine 3 cups water, sorghum, and 1 pinch of salt in a 2-quart saucepan. Bring to a boil over high; cook 5 minutes. Reduce heat to low; cover and cook for 1 hour, stirring once after 30 minutes. Remove from heat. Stir sorghum. Cover and let stand until more liquid is absorbed, 15 to 20 minutes. (The sorghum is done when the grains are chewy-firm with a slight snap.).
Meanwhile, heat 1/2 teaspoon oil in a large nonstick skillet over medium-high. Add half of the mushrooms, and spread in an even layer. Season with 1/8 teaspoon salt and 1/8 teaspoon pepper. Sear 3 minutes, stirring when bottoms of mushrooms are browned and tops are glistening with mushroom sweat. Cook, stirring often, until tender and fragrant. Transfer to a bowl. Repeat with remaining 1/2 teaspoon oil, remaining half of mushrooms, remaining 1/8 teaspoon salt, and remaining 1/8 teaspoon pepper.
Reduce heat to medium-low; add shallot, white scallion slices, and 1 tablespoon butter to skillet. Cook until soft and fragrant, about 2 minutes. Add to mushrooms.
Drain sorghum, reserving 2 to 3 tablespoons cooking liquid.
Melt remaining 1 1/2 tablespoons butter in skillet over medium. Whisk in the miso. Add the sorghum and reserved cooking liquid; stir to combine. (If mixture is too creamy, cook for a few minutes more to evaporate some of the liquid.) Stir in the mushroom mixture. Cook until warmed through. Stir in the green scallion slices. Serve warm or at room temperature.