Place potatoes in a large pot and cover with cold water. Bring to a boil, reduce to a simmer and cook until just cooked through, about 20 minutes. Strain and allow to cool. Remove skin with a paring knife, cut into 1-inch pieces, and set aside.
Heat canola oil in a large heavy-bottomed pot to 325 degrees F.
Carefully fry the potatoes until just cooked and a light tan color, about 5 minutes. Remove with a slotted spoon and set aside to dry on a sheet pan or plate lined with paper towels.
Increase the heat of the oil to 475 degrees F. Return the potatoes to the oil and fry until golden and crispy, about 2 minutes. Remove from the oil with a slotted spoon and drain on the paper towel-lined plate. Season generously with salt and smoked Spanish paprika.