Cook & dry noodles: Bring a kettle of water to a boil. Transfer dry vermicelli noodles to a bowl. Pour hot water over the noodles and let steep until softened, 1–2 minutes. Drain and transfer noodles to a bowl of cold water to stop them from further softening. With your hands, carefully squeeze as much liquid out of the noodles as possible. Transfer noodles to a clean kitchen towel and wring out excess water one more time.

Cut noodles: Use kitchen scissors to cut vermicelli noodles into 2-inch long strands. Transfer to a large bowl and set aside.

Rehydrate mushrooms: In a separate bowl, soak wood ear mushrooms in hot water until soft. With your hands, squeeze all the water out and slice mushrooms into thin, 2-inch long strips. Add to the bowl with the cut vermicelli noodles.

Finish filling: Add pork, shrimp, carrot, shallots, fish sauce, sugar, white pepper, and salt to the bowl with the noodles and mushrooms. Crack the egg into the bowl and mix until you get a bouncy, homogenous mixture.

Prepare work station: In a wide, shallow bowl or skillet, combine water and sugar, stirring until sugar is dissolved. Place the bowl near your rice paper wrappers, filling, and work surface.

Form rolls: Slide a piece of rice paper into the sugar water. Let sit until both sides are moist, about 5 seconds. Transfer to the kitchen towel. Let sit for 1 minute to soften. Center 3–4 tbsp of filling over the lower third of the wrapper. Lift the bottom edge to cover the filling. Tuck it tight and make sure it’s free of air pockets. Crease and fold in the left and right sides, sealing the edges. Roll forward, keeping it tight and free of air.

Transfer rolls to the fridge and let sit, uncovered, for 30 minutes.

Fry rolls: Heat oil in a Dutch oven or heavy-bottomed pot to 325°F or 160°C over medium-high heat. Working in batches, add rolls to the hot oil, seam side down. Fry rolls until golden and crispy, about 4–6 minutes.

Serve: Serve cha gio immediately in a platter with lettuce, mint, and cilantro. To make nuoc cham, combine fish sauce, lime juice, white vinegar, and sugar in a wide dipping bowl. Stir to dissolve sugar. Add chilies and garlic.