Heat a large nonstick skillet or wok over medium-high heat. Add 1 teaspoon coconut oil and swirl to coat the pan.
Add the chopped scallion whites and 1 tablespoon Thai green curry paste to the hot oil; sauté, stirring, about 1 minute until fragrant.
Add the minced garlic and 1 pound peeled, deveined shrimp to the pan; season with salt to taste and cook, stirring occasionally, about 2–3 minutes, until the shrimp begin to turn pink and opaque.
Pour in 6 ounces light canned coconut milk and add 2 teaspoons Thai fish sauce; stir to combine and bring to a gentle simmer.
Simmer 2–3 minutes more, stirring occasionally, until the shrimp are fully cooked through and the sauce is slightly reduced.
Remove the pan from the heat and stir in the chopped scallion greens and 2 tablespoons chopped fresh basil.
Taste and adjust salt if needed, then serve immediately.