Cook beans in large pot of boiling salted water until crisp-tender, about 3 minutes. Drain. Cut 2 inches from bottom of each lemongrass stalk; discard tops. Thinly slice bottom pieces; place in processor. Add next 5 ingredients, chopped basil, and 1/4 cup water. Blend until paste forms.
Heat oil in large skillet over medium-high heat. Add curry paste; cook, stirring often, until dry, 2 to 3 minutes. Stir in coconut milk; bring to simmer. Add shrimp; reduce heat to medium-low and simmer until shrimp are just opaque in center, about 5 minutes. Add green beans; stir to heat through. Season curry with salt and pepper. Transfer 2 cups curry to bowl; cover, chill and reserve for quesadillas. Transfer remaining curry to serving bowl; garnish with basil. Serve with lime wedges and Fresh Orange-Apple Chutney.