Heat the oil in a large pot and saute the mushrooms, garlic and ginger for 2 minutes over low to medium heat.: The pan should emit a soft sizzle and the olive oil will shimmer as the shiitake mushrooms start to release their moisture, creating a savory steam. You will smell the garlic and ginger bloom, sweet and slightly pungent, which signals that the aromatics are marrying into the oil. Visually, the mushrooms will darken at the edges and give up glossy juices that coat the pan. If you rush this step on high heat the garlic can char and taste bitter, so keep the temperature controlled and stir frequently to avoid hot spots.
Add the chicken broth, sesame oil, soy sauce, salt, scallion whites, carrots, bring to a boil and reduce to a simmer.: When you pour in the stock , the pot will steam up and the combined aromas of toasted sesame oil and soy sauce will deepen into a rounded, savory scent. Bubbles should climb steadily as you bring the liquid to a boil, then settle into gentle movement when reduced to a simmer. The carrots will become tender and impart sweetness into the broth, and the scallion whites will soften and release oniony notes. Boiling aggressively can make the broth cloudy and break apart delicate ingredients later, so reduce to a gentle simmer once it reaches a boil.
Add potstickers or dumplings, cover and simmer for 4-5 minutes or until cooked through.: As you nestle the frozen potstickers into the simmering broth, they will cool the surface briefly, then the pot will return to a gentle simmer with quiet popping sounds. The dumpling skins will swell and become translucent, and you may see a faint puff as the filling cooks. Timing matters because undercooked dumplings are doughy, and overcooked ones can burst and become mushy. Keep the heat steady, cover the pot to trap steam, and check one dumpling at the minimum time to ensure it is hot in the center.
Stir in spinach, divide into bowls and top with scallion greens, sesame seeds and additional sesame oil if desired.: When you stir the spinach into the hot broth, it will wilt almost instantly, losing volume and brightening in color. You should notice a fresh, green aroma mixing with the savory broth. Serve quickly so the greens remain tender yet vibrant. Finish with the reserved scallion greens for a pop of sharpness, a sprinkle of toasted sesame seeds for texture, and a tiny drizzle of toasted sesame oil if you want more aroma. Avoid letting the soup sit too long before serving or the greens and dumplings will continue to soften beyond the preferred texture.