To make the dumplings: Bring a large saucepan of salted water to a boil. Fill a large bowl with ice and water. Plunge the pea shoots into the boiling water and cook until bright green and crisp-tender, about 2 minutes. Drain and immediately transfer to the ice water. Drain well and squeeze out any excess liquid.
Meanwhile, place the mushrooms in a medium heatproof bowl and cover with boiling water. Let stand until softened, about 40 minutes. Drain well, trim off and discard the stems, and squeeze out any excess liquid from the caps.
In a large skillet, heat 1 teaspoon oil over medium heat. Add the leeks, season with salt and pepper, and cook, stirring occasionally, until tender but not browned, about 5 minutes. Remove from the heat and let cool completely.
Place the pea shoots in a food processor and pulse until chopped, with no pieces larger than 1 inch (2.5 cm). Transfer to a large bowl. Place the mushrooms in the processor (no need to clean it) and pulse until finely chopped. Add to the pea shoots along with the goat cheese, leeks, peas, oyster sauce, sugar, garlic, ginger, and ¼ teaspoon each salt and pepper.
Stir the filling well with a rubber spatula until evenly mixed.
Take out five wrappers and cover the rest with a damp dowel. Lay out the five wrappers like ducks in a row. Wet ½ inch of the rim of each wrapper. Scoop a level tablespoon of filling into the center of each wrapper, shaping it elongated like a football to make it easier to fold. Fold the wrapper in half like a taco and pinch the edges at the top center. Continue folding the dumpling using your preferred folding method (simply press the edges together or pleat to create another shape–I used the “Buddah’s Belly” fold from the book).
At this point, the dumplings can either be cooked immediately, covered and refrigerated for up to a couple hours, or frozen.
To pan-fry the dumplings, use a medium or large nonstick skillet (or cook two batches at the same time using two pans). Heat the skillet over medium-high heat and add 1 ½ tablespoons oil for a medium skillet and 2 tablespoons for a large one. Place the dumplings 1 at a time, sealed edges up, in a winding circle pattern. The dumplings can touch. Medium skillets will generally fit 12 to 14 dumplings, large skillets will fit 16 to 18 dumplings. Fry the dumplings for 1 to 2 minutes until they are golden or light brown on the bottom.
Holding the lid close to the skillet to lessen splatter, use a measuring cup to add water to a depth of roughly ¼ inch (about ⅓ cup water). The water will immediately sputter and boil vigorously, Cover with a lid or aluminum foil, lower the heat to medium, and let the water bubble away for 8 to 10 minutes, until it is mostly gone. When you hear sizzling noises, remove the lid as most of the water is now gone. Let the dumplings fry for another 1 or 2 minutes, or until the bottoms are brown and crisp. Turn off the heat and wait until the sizzling stops before using a spatula to transfer dumplings to a serving plate. Display them with their bottoms facing up so they remain crisp. (Alternatively you may steam these dumplings in a bamboo steamer basket lined with parchment paper or cabbage leaves.)
To make the Mimi Dip: In a microwave-safe bowl, heat the sugar with 2 tablespoons water for 30 seconds. Stir well until the sugar dissolves. Let cool to room temperature, then stir in the mayonnaise and sriracha. The dip can be refrigerated in an airtight container for up to 3 days.
Serve the dumplings with the Mimi Dip.