Rice Vermicelli with Chicken and Nuoc Cham

INGREDIENTS

• 1 1/2 skin-on, bone-in chicken breasts (about 2)
• Kosher salt
• 1 large shallot, thinly sliced crosswise, separated into rings
• 1/2 vegetable oil
• 8 rice vermicelli noodles
• 1 Fresno chile or red jalapeño, with seeds, finely chopped
• 1 small garlic clove, finely grated
• 1/3 fresh lime juice
• 1/4 fish sauce (such as nam pla or nuoc nam)
• 2 light brown sugar
• 4 baby white turnips, trimmed, thinly sliced into rounds
• 4 radishes, trimmed, thinly sliced into rounds
• 1 1/2 fresh Thai or sweet basil leaves, divided