Toast coconut in a dry medium saucepan over medium heat, stirring often, until golden brown, 5–7 minutes. Transfer to a small bowl.
Wipe out saucepan. Combine oil and shallots in saucepan and set over medium-high heat. Cook, stirring often, until shallots are golden brown and crisp, 8–10 minutes. Using a slotted spoon, transfer shallots to paper towels to drain; immediately season with salt.
Reduce heat to medium and add ginger and garlic to saucepan. Cook, stirring occasionally, until browned in spots, about 4 minutes. Add tomato paste and cook, stirring constantly, until paste splits and color darkens slightly, about 2 minutes. Add tamarind concentrate, honey, and soy sauce and cook, stirring constantly, until glaze is smooth and just beginning to bubble, about 1 minute. Remove pan from heat; taste glaze and season with salt.
Place a rack in upper third of oven; preheat to 425°F. Place 1 fish on a cutting board and thoroughly pat dry inside and out with paper towels. Using a sharp knife, make slashes crosswise on a diagonal about every 2" along length of body (make sure to cut all the way down to the bones as this will help the fish cook evenly). Turn fish over and repeat process on the other side. Transfer fish to a parchment-lined baking sheet, then repeat with remaining fish.
Season both fish all over with salt. Brush both sides with about half of the glaze, leaving the garlic and ginger behind. Roast fish, brushing with remaining glaze halfway through, until glaze is sticky and flesh flakes easily with a fork, 16–20 minutes.
Arrange fish on a large platter or 2 smaller platters and scatter toasted coconut, crispy shallots, chiles, and mint evenly on top. Serve with lime wedges alongside for squeezing over.