Combine coconut milk, lime juice, lime zest, lemon grass, garlic, and shallot in a blender. Puree until smooth.
Refrigerate 1 1/4 cups of the puree for later use. Pour the rest into a large bowl; add shrimp. Cover and refrigerate until shrimp is marinated, 2 to 3 hours.
Bring brown rice and water to a boil in a saucepan while shrimp marinate. Reduce heat to medium-low, cover, and simmer until rice is tender and liquid has been absorbed, 45 to 50 minutes.
Heat olive oil in a skillet over medium-high heat. Add edamame and snow peas; saute until tender but still crispy, 3 to 5 minutes. Add the 1 1/4 cups of reserved puree and bring to a simmer.
Add shrimp and marinade to the sauce in the skillet; cook until shrimp are firm and no longer pink, 8 to 10 minutes. Serve over the cooked rice.
