Preheat the oven to 425ºF. Prepare the leeks by cutting off the root end and slicing the white and pale green parts into 1-inch sections. Toss them with a tablespoon or so of oil. Prepare a baking sheet with a sheet of aluminum foil, oil it lightly, then stand the leeks, one cut end down, on the sheet. Roast for about 10 minutes, then turn the leeks over to stand on their other cut sides and roast for another 10-12 minutes, until they are turning golden brown and softening. Remove from the oven and set them aside. When they are cooled a bit, remove the tough outer layer.
While the leeks are in the oven, prepare the spice paste by putting all the components into a food processor or blender and zap them until the paste is smooth and uniform. Add a bit of water if it seems too thick and uncooperative.
Heat 3 tablespoons of oil to medium in a large skillet (or a wok). Add the spice paste and cook it, stirring now and then, for about 15 minutes. Then add in the coriander, stir-fry for about 30-45 seconds, and then add in the coconut milk. Stir well, bring everything to a boil, and then simmer for 15 minutes. Add the lime juice and fish sauce, stir again, and taste. You may want to add a bit of salt. Finally, gently stir in the leeks and heat everything. That's it. You're ready to serve. We served this with steamed white rice, but it would be lovely on its own.