Mix together the oil, cumin, paprika and cinnamon in a small bowl. Let sit at room temperature while you prepare the potatoes.
Put potatoes in a medium saucepan over medium heat, and cover with cold water. Bring to a boil, and cook until potatoes are tender, but still firm, about 15 minutes. Drain and let cool slightly before cutting crosswise into 1/2-inch thick slices.
Preheat a grill pan over medium heat. Brush the potatoes on each side with the spice oil and season with salt and pepper, to taste. Grill until lightly golden brown on each side and just cooked through, about 3 minutes per side. Continue to brush with the remaining oil, as they grill. Transfer to a serving platter and serve.