Make the dumplings - In a large bowl, combine all ingredients. Using a fork, mash all ingredients to form a paste. Stir until well combined.
On a work surface, place dumpling wrappers and spoon 1 tablespoon of filling in the center of each. With fingertips, moisten the edges of the wrappers. Pleat edges of the wrapper, pinching the edge closed after each pleat and the entire dumpling is sealed. Then, pinch and twist top to seal.
In a large nonstick skillet on medium to low heat, add 2 tablespoons vegetable oil. When hot, add dumplings and fry for 30 to 60 seconds. Add a quarter of a cup water, cover with lid. Cook for an additional 1 to 2 minutes. Remove to plate. Repeat with remaining dumplings.
Make the green beans - In a cast iron skillet on medium to high heat, add vegetable oil. Toss in green beans and sauté for 1 minute. Stir in garlic and ginger, cooking for another minute. Set aside.
Make the sauce - In a mixing bowl, whisk together all ingredients. Stir well. Set aside.