Place 2.5 ounces mung bean vermicelli and 1/4 cup dried wood ear mushrooms into two separate bowls. Cover each generously with hot water and let them soak for 20-30 minutes (while you're waiting, you can prep the other ingredients).
Drain the soaked vermicelli and wood ear mushrooms and chop each coarsely, then transfer them to the bowl of a food processor. Add the chopped shallots and pulse the food processor until they are all finely chopped. Add 1 pound ground turkey, the grated carrots, minced garlic, grated ginger, 2 Tablespoons fish sauce, 1 Tablespoon canola oil, 1 teaspoon granulated sugar, 1 teaspoon kosher salt (or MSG-salt), and 1/4 teaspoon white pepper powder to the food processor and process until everything is evenly mixed (don't overprocess - I recommend using low speed if possible).
Dissolve 2 teaspoons granulated sugar in 1 cup water in a large plate or other shallow dish like a baking pan (make sure that your rice paper is able fully fit in the bottom).
Working with 1 piece of rice paper at a time, fully immerse the paper into the water for about 5 seconds, then remove it and shake off excess water. Lay the wet paper on a cutting board. Scoop about 1/4 cup of the turkey mixture on the rice paper about 1/4 of the way up from the bottom edge and form it into a roughly 4-5" long log. Fold the bottom edge of the rice paper up over the meat, then the sides, then roll it up towards the top. Repeat with the remaining rice papers and meat.
Place the wrapped spring rolls onto a cooling rack placed in a baking sheet and place them uncovered in the fridge for at least an hour (if you plan to leave them for longer than 2 hours, I recommend covering them loosely with plastic wrap.)
When you're ready to cook the spring rolls, remove them from the fridge, and spray or brush them completely with a very thin layer of canola or other neutral-flavored cooking oil. Place them in an air fryer basket or rack and ensure that they're not touching.
Air fry the spring rolls at 425°F for 10 minutes. Flip the spring rolls, then air fry for another 10 minutes (they should be well-browned and crispy on the outside). Serve with nuoc cham, Thai sweet chili sauce, or sriracha.
Easy Nuoc Cham (Fish Sauce Dipping Sauce)
In a small bowl or measuring cup, stir together 2 Tablespoons granulated sugar, 2 Tablespoons lime juice, 2 Tablespoons fish sauce, 4 Tablespoons cold water, 1 teaspoon chile garlic sauce, and 1 small clove garlic until the sugar is dissolved. Taste the sauce. If it's too strong for you, add an additional 1-2 Tablespoons of water. Refrigerate until ready to use. Keep leftovers in an airtight container in the fridge.