Put the wings in a large bowl, followed by honey, olive oil, salt, garam masala, cumin, paprika, and cayenne. Toss to combine, then transfer to a zip-top bag. Let rest 30 minutes, overnight, or up to several days in the refrigerator.
Bring 2 cups of water to a simmer in a small saucepan, then add the asafoetida, ginger, cayenne, and garam masala. Meanwhile, toast cumin and fennel in a small skillet until they're fragrant and slightly smoky. Transfer to a small bowl to cool, then grind the seeds in a mortar and pestle until they're coarse and sandy. Add to water-and-spice mixture, followed by the sugar, and stir to combine. Add tamarind and continue cooking for 20 minutes.
Preheat oven to 400 degrees F. After 20 minutes, check chutney for consistency—it should look like a chocolate sauce. Remove from heat to cool. Meanwhile, line a rimmed baking sheet with aluminum foil; place a wire rack on top of the baking sheet and arrange the marinated chicken wings in a single layer. Bake 20–25 minutes. Remove from oven and transfer wings to a large bowl. Toss with the chutney, then replace wings on the rack and bake again, 5–10 minutes, until golden brown.