Peel the ginger, then mince or grate along with 1 clove garlic. Trim the green beans. Thinly slice the scallions and the remaining garlic. In a medium bowl, thoroughly combine the minced garlic, ginger, scallion, ground beef, and a large pinch of salt and pepper. Set aside.

Fill a small bowl with water and keep it near your work station. Working one at a time, spoon 1 teaspoon of the beef mixture into the center of each wonton wrapper, starchy side-up. Then, wet your finger to dampen the edge of the wonton wrapper. Fold over one corner onto the other; press edge to seal. Make sure to eliminate any air pockets. Repeat until filling is used up. Cover the gyozas with a damp towel and set aside.

In a small bowl, mix together 3 tablespoons soy sauce, 2 tablespoons sugar, and as many chili flakes as you dare (we used 1/4 teaspoon). Set aside.

In a large pan, heat 1 tablespoon oil over medium-high heat. Working in batches, cook the gyozas for about 1 minute per side, until golden brown. Set aside and repeat. Once all the gyozas are seared, return them to the pan. Reduce the heat to low and carefully pour 1/3 cup water in the pan. Cover and simmer for about 6 minutes. Uncover and continue cooking for another 2 minutes over medium-high heat to crisp them up.

Meanwhile, heat 1 tablespoon oil in a large pan over medium heat. Add the sliced garlic to pan and cook for about 30 seconds, until fragrant. Add the green beans and cook, tossing for 1-2 minutes. Add 1/3 cup water to the pan and continue cooking until green beans are crisp-tender and water has evaporated, about 4-5 minutes. Add 2/3 of the soy mixture to the pan and cook until syrupy. Set aside, covered, to keep warm.

Serve the gyozas with a side of glazed green beans and remaining soy mixture. Sprinkle with sesame seeds and enjoy!