In a large skillet, bring 1-2 inches of water to a boil. Add the whole trimmed green beans to the skillet. Cook for about 2 minutes, until the green beans are bright green. Drain in a colander and run under very cold water or plunge into an ice bath to stop the cooking process. Pat the green beans dry, set them aside on a dish towel or plate, and dry out the skillet.
In the same skillet, melt the butter over medium-high heat. Add the garlic and stir until fragrant, about 30 seconds. Add the mushrooms and onion to the skillet; cook until soft, about 3 minutes. Reduce the heat to low. Stir in the tomatoes, brown sugar, soy sauce, vinegar, and green beans. Cook, stirring, until warmed through, about 1-2 more minutes. Taste and season with salt and pepper.
