Place the sweet potatoes in a pan, and fill with enough water to cover. Bring to a boil, and cook until potatoes are easily pierced with fork, about 10 minutes. Drain, place the potatoes in a mixing bowl, and mash.
Meanwhile, heat 1 tablespoon canola oil in a skillet over medium-high heat. Stir in the jalapeno pepper, green onions, and garlic. Cook and stir until the vegetables are soft, about 5 minutes. Stir the vegetables, brown sugar, and allspice into the mashed sweet potatoes. Season to taste with salt and pepper.
Form the sweet potato mixture into 12 slightly flattened cakes about 2 to 2 1/2 inches in diameter using your hands or large spoons. Place on a plate.
Heat 1/4 cup canola oil in a skillet over medium-high heat. Place the sweet potato cakes in the skillet, four at a time, and cook, turning once, until golden brown on each side, 6 to 8 minutes. Add more oil if needed.
