Preheat oven to 450° and line a small baking sheet with parchment paper. Cut ends off squash, then cut in half lengthwise and scoop out seeds. Drizzle olive oil over squash and season with salt and pepper. Place squash, cut side down on prepared baking sheet and bake until a knife inserted in the thickest part meets no resistance, about 40 minutes. Let cool.

When squash is cool enough to handle, scoop out flesh into a large bowl and mash with a fork until smooth. You should have about 2 cups of puree.

Add ginger, garlic, green onions, soy sauce, vinegar, and red pepper flakes to squash and stir to combine. Taste and season with salt and pepper to taste.

Fill a small bowl with water. Work with one wrapper at a time and keep remaining wrappers covered with a damp paper towel. Place a wrapper on a clean surface and place a heaping teaspoon of filling in center of wrapper. Dip your finger in water and wet all edges of wrapper.

Seal wrapper together by making folds starting on one end and working your way towards the other end. Use more water to help seal dumplings tightly. Repeat with remaining wrappers and filling.

In a large skillet over medium-high heat, heat 2 tablespoons vegetable oil. Add potstickers, seam side up in a single layer, working in batches as needed. Sear for 2 minutes or until bottoms are golden. Reduce heat to low and very carefully add ¼ cup water (it will splatter!). Cover with a lid and let steam for 5 minutes or until wrappers are soft. Remove from pan and carefully wipe pan dry and repeat with remaining potstickers.

For dipping sauce: In a small bowl, combine all ingredients.

Serve potstickers with dipping sauce.