Place ⅔ cup raw cashews in a small bowl and pour in hot water to cover. Let sit until softened (you should be able to crush a nut easily between 2 fingers), 15–20 minutes.
Meanwhile, finely grate 2 garlic cloves and half of one 2″ piece ginger, peeled, into a medium bowl. Add 1½ lb. skinless, boneless chicken thighs, excess fat trimmed, cut into 2″ pieces, and 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt and toss to combine. Let chicken sit while you make the sauce.
Drain cashews and transfer to a blender. Coarsely chop remaining 1″ piece ginger, peeled. Add ginger, 1 small jalapeño, halved, 2 Tbsp. fresh lime juice, 1 tsp. cumin seeds, ½ tsp. ground turmeric, remaining 3 garlic cloves, remaining 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt, and 1½ cups water to blender and blend until smooth. Set cashew sauce aside.
Heat 1 Tbsp. vegetable oil in a large skillet over medium-high. Cook chicken, tossing occasionally, until cooked through, about 3 minutes. Add reserved cashew sauce and cook, stirring occasionally, until sauce is slightly thickened, about 3 minutes.
Divide steamed rice among shallow bowls and spoon cashew chicken over; top with cilantro sprigs. Serve with lime wedges for squeezing over.