Heat oil in a large saucepan over medium heat. Add curry paste, garlic, ginger and lemongrass; cook, stirring constantly, until the mixture is aromatic and dry, about 2 minutes. Add coconut milk and broth; stir to loosen any browned bits from the bottom of the pan. Bring to a boil over medium-high heat. Reduce heat to medium-low; simmer, undisturbed, for 5 minutes.
Stir fish sauce and cornstarch in a small bowl. Stir into the curry mixture; bring to a boil over high heat. Reduce heat to medium-low; simmer, stirring occasionally, until the sauce begins to thicken, about 5 minutes.
Add snow peas and carrots to the curry mixture; return to a boil over medium-high heat. Boil, undisturbed, until the vegetables are tender, about 2 minutes. Add shrimp; cook, stirring occasionally, until the shrimp turn pink and are cooked through, about 2 minutes. Remove from heat; stir in basil. Serve over rice. Recipe developed by Jasmine Smith
