- 1 1/2 pound skin-on, bone-in chicken breasts (about 2)
- Kosher salt
- 1 large shallot, thinly sliced crosswise, separated into rings
- 1/2 cup vegetable oil
- 8 ounces rice vermicelli noodles
- 1 Fresno chile or red jalapeño, with seeds, finely chopped
- 1 small garlic clove, finely grated
- 1/3 cup fresh lime juice
- 1/4 cup fish sauce (such as nam pla or nuoc nam)
- 2 tablespoons light brown sugar
- 4 baby white turnips, trimmed, thinly sliced into rounds
- 4 radishes, trimmed, thinly sliced into rounds
- 1 1/2 cups fresh Thai or sweet basil leaves, divided
- Prepare grill for medium heat. Season chicken with salt and grill, turning often and moving away from direct heat if needed, until cooked through and an instant-read thermometer inserted into the center registers 165°, 20-25 minutes. Transfer chicken to a plate. Let cool slightly, then shred meat, discarding skin and bones. Set aside.
- Cook shallot in oil in a small saucepan over medium heat, stirring occasionally, until shallot is golden brown and crisp, 8-10 minutes (reserve shallot oil and use to make vinaigrettes). Using a slotted spoon, transfer shallot rings to a paper towel-lined plate and season with salt. Set aside.
- Meanwhile, place noodles in a large bowl and add boiling water to cover. Let noodles soak until tender but not mushy, 5-10 minutes; drain. Rinse under cold water and drain well.
- Mix chile, garlic, lime juice, fish sauce, and brown sugar in a large bowl to combine. Add noodles, turnips, radishes, half of basil, and reserved shredded chicken, and toss to combine. Top with reserved fried shallot rings and remaining basil.
- DO AHEAD: Shallot rings can be fried 3 days in advance. Store airtight at room temperature. Dressing can be made 2 days ahead.