Spread the wings in a single layer on wire rack set over a rimmed baking sheet and season liberally with salt and pepper. Refrigerate at least 1 hour, or preferably overnight.
Heat 2 inches of oil in a large, heavy-bottomed pot over medium heat until a deep-fry thermometer registers 275 degrees F. Working in 2 batches, fry the wings, tossing occasionally, until pale brown and cooked through, about 20 minutes per batch. To test for doneness, lift a wing from the oil and pierce with a paring knife. If there is no resistance they are done. Transfer the wings with a slotted spoon to a clean rack set over a baking sheet and let cool for at least 30 minutes. (Make sure the oil returns to the proper temperature between batches.)
Meanwhile, make the sauce: Heat 2 tablespoons vegetable oil in a medium pot over medium heat. Add the garlic, onion and chile and cook, stirring occasionally, until soft and lightly golden, about 12 minutes. Add the tomato paste and cook, stirring until lightly caramelized, about 2 minutes. Stir in the peanut butter and bay leaf, then pour in the broth. Bring the mixture to a simmer then cook, stirring often, until it is thickened and slightly reduced, about 8 minutes. Remove the sauce from the heat, discard the bay leaf and stir in the fish sauce. Finely grate the zest of 1 lime into the sauce, then add its juice. Season the sauce with salt and pepper, then pour it into a blender and puree until very smooth. Transfer the sauce to a small saucepan and keep warm.
Increase the temperature of the frying oil to 425 degrees F. Working in 3 batches, fry the wings again until the skin is golden brown and very crisp, about 3 minutes per batch. Transfer the wings to a large bowl and season each batch with salt while hot. (Make sure the oil returns to the proper temperature between batches.)
Pour two-thirds of the reserved peanut sauce over the wings and toss to coat evenly. Transfer the wings to a platter and sprinkle with the peanuts. Finely grate the zest of another lime over the wings then cut the remaining limes into wedges. Serve the wings immediately with lime wedges, sliced mango and extra peanut sauce on the side.
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