Heat 1 tablespoon of oil in a large saute pan on high heat. Add the shrimp and saute until pink on both sides, about 4-5 minutes. Season the shrimp with salt and pepper and set aside.
In the same pan, heat the remaining 1 tablespoon of oil over medium heat. Saute garlic and ginger until aromatic, about 30 seconds. Add shallot sauce, tomato paste, soy sauce, rice vinegar, and brown sugar, stirring until combined. Simmer for 2 minutes or until the sugar has dissolved.
Add the shrimp to the shallot sauce and fresh Thai basil and toss to combine. Top the shrimp with toasted coconut. Serve immediately with rice if desired.
Notes
You can find Bull's head shallot sauce at Asian markets such as 99 Ranch.