Prep the vegetables by washing and slicing the bell pepper into strips, cutting the carrot into thin matchsticks, and trimming the ends of the snap peas. In a bowl, whisk the soy sauce, sesame oil, rice vinegar, optional chili paste, sugar, and cornstarch slurry until smooth.

Heat 1 to 2 tablespoons of cooking oil in a large skillet over medium-high heat. Once shimmering, arrange your potstickers flat side down in the pan without overcrowding. Fry for 3 to 4 minutes until golden brown and crispy on the bottom, then add ¼ cup of water. Cover the pan and let them steam for another 3 to 4 minutes. Uncover and cook for an additional 1 to 2 minutes to re-crisp the bottoms.

Push the potstickers aside in the skillet. Add the minced garlic and ginger, stirring quickly for about 30 seconds until fragrant. Toss in the bell pepper and carrot matchsticks, cooking together for 2 to 3 minutes. Add the snap peas and stir-fry for an additional 1 to 2 minutes until crisp-tender.

Pour the sauce mixture over the vegetables and potstickers in the skillet. Toss to coat everything evenly. Let simmer for 1 to 2 minutes, allowing the sauce to thicken. Garnish with sliced green onions and sesame seeds before serving.