Pat dry the shrimp with a kitchen towel and season the shrimp with red curry paste, soy sauce, curry powder, salt, and black pepper. Toss it until well combined.
Heat a skillet over medium heat; add oil and once the oil is heated add the seasoned shrimp and cook for 4-5 minutes until the shrimp is cooked through and opaque. Transfer the shrimp to a plate and set it aside.
To the same skillet, add the butter; once the butter is melted, add garlic, ginger, and shallots. Cook for 2 minutes until onions are soft.
Deglaze the skillet with chicken broth and stir in the red curry paste and soy sauce.
Add the spices; brown sugar, curry powder, coriander powder, turmeric powder, salt, and pepper. Let it simmer for 2-3 minutes.
Pour in the canned coconut milk and bring the sauce to a boil. Lower the heat and allow the sauce to simmer for 5 minutes until the sauce starts to thicken.
Transfer the shrimp back to the skillet and allow the shrimp to cook for 2 minutes in the curry.
Add lime juice and Thai basil and remove the skillet from the heat.
Garnish the coconut shrimp curry with cilantro and serve it over basmati rice to enjoy.