Heat the oil in large skillet set over medium heat. Add the shallot, garlic and ginger and cook 1 to 2 minutes. Mix in the curry powder and cook 1 minute more. Add the coconut milk/cornstarch mixture, lime juice and brown sugar.
Bring to a simmer and simmer until the coconut milk is thickened by the cornstarch. Add the prawns and simmer until just cooked through, about 3 to 4 minutes. Halve and thinly slice each avocado. Fan a half avocado on each of 4 plates. Divide and top with prawns and sauce, and serve.