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In a skillet, heat 2 tablespoons of the oil over high heat until shimmering. Add the onion and let sizzle, stirring occasionally, for 1 minute. Stir in the saffron, lower the heat to medium, and cook, stirring occasionally, for 5 minutes. Lower the heat to low and cook until the onions are completely soft but have not started to brown, 6 to 8 minutes more. Set aside.
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Bring a large pot of salted water to a boil. Peel and slice the potatoes into 1⁄3-inch-wide rounds, add the sliced potatoes to the pot, and cook until tender, about 6 minutes. With a slotted spoon, transfer the potatoes to a baking sheet to cool.
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In a small bowl, whisk together the lemon juice, garlic, and paprika, then whisk in the remaining 4 tablespoons oil.
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When the potatoes have cooled but are still warm, overlap them slightly on a platter. Nestle the saffron onions in and around the potato slices. Squeeze the juice from the lemon over the potatoes and sprinkle with salt. Drizzle the vinaigrette over the potatoes and onions and sprinkle with the pine nuts and parsley leaves. Season to taste with salt and pepper and serve.