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.
Notes
Boil the green beans just until they're crisp-tender (about 2 minutes). Don't overcook them or they will become soft and mushy and turn a greenish-brown color.
Plunge the green beans into an ice water bath or run them under very cold water until they're nice and cool. This stops the cooking process so that they maintain that beautiful bright green color.
Adjust the seasoning to suit your taste preferences. Add more salt and pepper, or try some fresh herbs or dried herbs. Good options include basil, thyme, parsley, oregano, rosemary, or chives. You can make the green beans and mushrooms spicy with a pinch of crushed red pepper flakes, too.
Garnish the green beansand mushrooms with shaved or grated Parmesan cheese for even more flavor.