Place a large skillet or nonstick wok over medium-high heat. Add 2 tablespoons of high-heat oil. The oil should ripple slightly when hot.

Carefully place the frozen potstickers into the hot pan in a single layer, ensuring the flat side is down. Do not overcrowd; work in batches if necessary. Sear for 2 to 3 minutes until the bottoms are golden brown and perfectly caramelized.

Once the bottoms are crispy, carefully pour 1/2 cup of broth or water into the pan. Immediately cover the pan with a tight-fitting lid. This traps the steam, cooking the rest of the dumpling filling thoroughly. Reduce the heat to medium. Steam for 5 to 7 minutes (check packaging for exact time), or until the liquid has almost evaporated.

Once the liquid is gone and the potstickers are plump, remove them from the pan and set them aside on a plate. The pan’s surface should be relatively dry.

Add the remaining 1 tablespoon of sesame oil to the now-empty pan. Add the minced garlic, grated ginger, and the white parts of the scallions. Stir and cook for about 30 seconds until fragrant. Be careful not to burn the garlic.

Add the carrots, bell peppers, and mushrooms (if using) to the pan, stirring constantly. Stir-fry for 3 to 4 minutes until they begin to soften but still have a good snap to them (crisp-tender). If using sugar snap peas, add them during the last minute of this stage.

While the vegetables cook, whisk together the ingredients for the sauce: soy sauce, rice vinegar, honey, and the remaining 1/2 cup of broth until smooth. Set aside the cornstarch slurry for a moment.

Pour the prepared sauce over the vegetables, stirring constantly to coat everything. Bring the sauce to a gentle simmer.

Give the cornstarch slurry a quick re-stir, then pour it slowly into the simmering sauce. Stir continuously for 30 to 60 seconds. The sauce will transform into a glossy, thick glaze.

Return the crispy potstickers to the pan. Gently toss them in the glossy sauce for about 30 seconds, just long enough to coat them thoroughly without disturbing the crispy bottom crust. Garnish immediately with the reserved green scallions, toasted sesame seeds, and chopped peanuts or cashews. Serve immediately over rice.