Bring a large pot of water to a boil. Add the 12 ounces soba noodles and cook, stirring occasionally, until tender, about 4 minutes. Drain and rinse the noodles under cold water. Transfer the noodles to a large serving bowl.
In a medium bowl, combine 2 tablespoons of the 1/4 cup sesame oil with the 2 tablespoons low-sodium soy sauce. Pour this sauce over the noodles and toss to coat.
Line a plate with paper towels. Heat 1 tablespoon of the sesame oil in a large skillet over medium heat. Add the thinly sliced shallot and the 2 teaspoons grated fresh ginger. Cook, stirring, until the shallots are golden brown and crisp, about 3 minutes. Use a slotted spoon to transfer the shallot-and-ginger mixture to the paper towel–lined plate to drain.
Reduce the heat to very low. Add the 8 coarsely chopped garlic cloves to the same skillet and cook, stirring, until the garlic is golden, about 2 minutes. Transfer the garlic to the paper towel–lined plate.
In a bowl, combine the zest and juice of one large lime with the remaining sesame oil (the remaining 1 tablespoon). Add the 1 pound large shrimp to that bowl and season with salt to taste; toss to coat.
Return the skillet to medium-high heat. Add the shrimp (and any juices from the bowl) to the skillet and cook until pink and opaque, about 1 minute per side.
Add the 3 finely chopped scallions, 1/2 cup chopped cilantro, 1/2 teaspoon crushed red pepper, the fried shallot-and-ginger mixture, the fried garlic, and the cooked shrimp to the bowl of noodles. Gently toss to combine.
Serve immediately with lime wedges. You may also chill the noodles until needed and serve cold.