Combine 1/2 cup rice vinegar, the sugar and 1 teaspoon salt in a small saucepan. Bring to a boil, stirring to dissolve the sugar; turn off the heat. Put the cucumbers, radishes, turnip and jalapeño in a small bowl and pour the vinegar mixture on top; set aside at least 20 minutes.
Meanwhile, combine all but 1/2 cup scallions with the remaining 2 teaspoons rice vinegar, the ginger, soy sauce and 1 1/2 teaspoons salt in a medium heatproof bowl. Heat the vegetable oil in a small saucepan over medium-high heat until shimmering, about 3 minutes. Pour the hot oil over the scallion mixture, stir and set aside until cool, 20 minutes. Transfer to a food processor and pulse several times to make a coarse paste.
Bring a large pot of salted water to a boil. Add the noodles and cook as the label directs. Drain and return to the pot. Add the ginger-scallion paste and toss to coat.
Divide the noodles among bowls. Drizzle the oyster sauce on top. Drain the vegetables from the pickling liquid and add to the noodles. Top with the reserved scallions.