In a medium bowl, whisk together the coconut milk, curry paste, lime juice, lime zest, fish sauce, honey, soy sauce, garlic, ginger, and red pepper flakes. Set aside.
Toss the chicken pieces with the cornstarch, salt, and pepper until evenly coated.
Heat the neutral oil and sesame oil in a large skillet or wok over medium-high heat until shimmering. Add half the chicken in a single layer and cook 3 to 4 minutes per side, until golden and cooked through to 165°F (74°C). Transfer to a plate and repeat with the remaining chicken.
Add the red onion and shiitake mushrooms to the skillet. Cook 3 to 4 minutes, until softened and lightly browned. Add the snow peas and cook 1 minute more.
Pour in the coconut-lime sauce and bring to a gentle simmer. Cook 4 to 5 minutes, stirring occasionally, until slightly thickened.
Return the chicken and any juices to the skillet. Toss to coat, then fold in the mango and half the cashews. Cook 1 minute more.
Taste and adjust with additional lime juice or honey as needed. Serve over jasmine rice, topped with the remaining cashews, toasted coconut, and fresh cilantro, with lime wedges alongside.