Place the noodles in a heatproof medium bowl and add hot water to cover. Cover the bowl and soak the noodles until hydrated, 8 to 10 minutes. Drain the noodles and transfer to a large rimmed baking sheet. Snip the noodles with kitchen shears a few times to break them up into slightly smaller pieces.

In a large skillet, heat 2 tablespoons of the olive oil over medium-high heat. Add the shredded mushrooms and toss to coat in the oil. Sear until the mushrooms start to soften and the underside is starting to brown, 4 to 5 minutes. Add ½ teaspoon of salt and toss again. Continue to sear and toss the mushrooms occasionally, until crisp and browned around the edges, 4 to 5 minutes. Transfer the mushrooms to the baking sheet with the noodles.

While the pan is still hot, add another 1 tablespoon of oil and swirl the pan to evenly coat. Add the cabbage and toss to coat in the oil. Stir-fry the cabbage until golden on the edges, 6 to 8 minutes, then transfer to the baking sheet.

Add the green onions, hoisin, sesame oil, remaining ½ teaspoon of salt, and white pepper to the filling mixture and toss to combine. Let the filling cool completely.

In a small bowl, stir together the flour and water to make a paste (you will use this to seal the spring rolls). Peel the spring roll wrappers apart. Working with one at a time, position a wrapper on a work surface in front of you, orienting it like a diamond so one corner is facing you. Place about ⅓ cup (50 g) of the filling just below the center of the wrapper. Press the filling into a 1 by 4-inch (2½ by 10 cm) log shape.

Lift the bottom corner of the wrapper and fold it up and over the filling. With your finger, tuck the wrapper back toward you, tightening it around the filling. Fold the left and right corners of the wrapper tightly over the filling. Brush some of the flour paste over the top corner of the wrapper and then tightly roll up the spring roll and press the seam to seal. Place the assembled spring roll on a rimmed baking sheet or plate and repeat with the remaining wrappers and filling.

Preheat the oven to 400°F and line a large baking sheet with parchment paper. Brush the baking parchment paper with oil. Arrange the spring rolls on the prepared baking sheet, spacing them 1 inch (2.5 cm) apart. Lightly brush the tops of each spring roll with olive oil. Bake until golden brown and crispy, 25 to 28 minutes. Let the spring rolls cool for a few minutes before serving.