Slice green onions, separating the white and reserving the green for garnish. Whisk together coconut milk, curry paste, fish sauce, and brown sugar.
Heat oil in a medium sauté pan over medium heat. Add whites of green onion and garlic. Sauté for one minute and add shrimp in a single layer. Cook shrimp 2 minutes per side and remove from pan.
Add coconut milk mixture to the pan and bring to a full simmer. Add snow peas and stir to coat. Allow to simmer uncovered about 4 minutes over medium/high heat. Stir once or twice until snow peas are just tender and the sauce has reduced to a syrupy consistency.
Toss shrimp back into the pan and stir to coat with sauce and warm throughout for about 1 minute. Season lightly with salt.
Serve immediately over rice and garnish with reserved sliced green onions, fresh cilantro and a squeeze of fresh lime juice.