Prick the sweet potatoes with a fork 4 or 5 times each. Microwave at high power for 10 to 15 minutes, until partially cooked (slightly softened but not cooked through). The time will depend on the size of the potatoes; check them often by squeezing them slightly during the cooking. Remove them from the microwave individually as they are done and set aside to cool.
Meanwhile, combine the pecans, brown sugar, cane sugar, cinnamon, nutmeg, allspice, salt, and 3 tablespoons of the nut oil in a large bowl and, with a rubber spatula, fold together until well mixed and the nuts are thoroughly coated with spices and oil.
In a 12-inch skillet, heat the remaining 2 tablespoons oil over medium high-heat until it begins to shimmer. Add the nut mixture and cook, stirring frequently for 7 to 8 minutes, until the sugar dissolves. Set aside.
When the potatoes are cool enough to handle, slice in ½-inch rounds.
Heat the oil and butter in a 12-inch skillet set over medium heat, until the oil shimmers and the butter has melted. Tilt the pan to coat, place the sweet potato rounds into it in a single layer, cook for 2½ to 3 minutes, and turn the rounds over. Continue to cook for 2½ to 3 minutes, until the potatoes are lightly browned and cooked through. Transfer to a serving platter and top with the glazed pecans.
Note: Nutmeg is available ground, but if you buy the whole nutmeg, and grate it or scrape it with a sharp knife yourself, the flavor and fragrance will be much stronger. Look for it in specialty spice stores, good supermarket spice sections, or online.