To make the dumpling dough, mix the flour and salt in a bowl. Gradually add water, mixing until a dough forms. Knead for 5 minutes until smooth. Cover with a damp cloth and let it rest for 15 minutes.
While the dough rests, prepare the filling. In a bowl, combine ground pork or chicken, chopped green onions, soy sauce, sesame oil, ginger, and garlic. Mix well and set aside.
For the smashed cucumber salad, cut the cucumbers into quarters lengthwise and then smash them with the flat side of a knife or a mallet to create craggy edges. Place in a mixing bowl.
In a small bowl, whisk together rice vinegar, sugar, salt, and pepper. Pour over the cucumbers and toss to coat. Set aside to marinate while you prepare the dumplings.
After the dough has rested, roll it out on a floured surface to about ⅛ inch thick. Cut into circles (about 3 inches in diameter).
Place a small spoonful of filling in the center of each circle. Fold over and pinch the edges to seal tightly. Make sure no filling leaks out.
In a large pot, bring water to a boil. Drop the dumplings in batches and cook for about 5-6 minutes or until they float to the surface. Remove with a slotted spoon and set aside.
To prepare the peanut sauce, whisk together peanut butter, soy sauce, lime juice, honey, and red pepper flakes in a bowl. Add warm water gradually, whisking until you reach your desired consistency.
Serve the dumplings hot alongside the smashed cucumber salad. Drizzle with peanut sauce before serving.