In a medium saucepan, bring the stock to a simmer. Add the shrimp, cover and simmer over moderate heat until just cooked, about 2 minutes.
With a slotted spoon, transfer the shrimp to a plate to cool. Cover the stock and keep it at barely a simmer.
In a medium saucepan, melt the butter in the olive oil. Add the garlic and onion and cook over low heat, stirring, until softened, about 4 minutes.
Add the rice and cook over moderate heat, stirring, until it is coated with oil, about 1 minute. Add the wine and simmer until almost evaporated, about 3 minutes. Add 1 scant cup of the simmering stock and cook, stirring constantly, until it is absorbed. Continue to add the stock, 1 cup at a time, stirring constantly until it is absorbed. The risotto is done when the rice is tender but still slightly firm and creamy, about 25 minutes total.
Stir in the shrimp. Remove the risotto from the heat and stir in the basil, goat cheese, Parmesan, ginger and lemon zest. Season the risotto with salt and pepper and serve.