Preheat oven to 425°F (220°C). Line a large baking sheet with parchment paper and place a wire rack on top for maximum crispiness.
Pat the chicken wings completely dry with paper towels to ensure the skin gets crispy.
In a large bowl, whisk together the olive oil, allspice, thyme, cinnamon, nutmeg, cayenne, sea salt, and black pepper.
Add the wings to the bowl and toss thoroughly until every wing is evenly coated in the spice rub.
Arrange the wings in a single layer on the wire rack, ensuring they aren't touching.
Bake for 35-40 minutes, flipping halfway through, until the wings are golden brown and the skin is crackling.
While the wings bake, prepare the salsa by combining the diced mango, red bell pepper, red onion, lime juice, and cilantro in a small bowl.
Let the salsa sit for at least 10 minutes to allow the flavors to meld.
Serve the hot, spiced wings immediately with the chilled mango salsa on the side or spooned over the top.