Heat oven to 200C/180C fan/gas 6. Peel the potatoes and cut into large chunks or, if they are small enough, keep them whole. Place in a pan of salted water, add most of the turmeric, stir and bring to the boil. Turn down the heat and simmer the potatoes for 6 mins until the sides are fluffy. Drain well and leave to cool slightly. Mix the flour, polenta, paprika and remaining turmeric together in a large bowl, then toss through the potatoes until evenly coated in the flour mix.
Put the oil and fat in a large roasting tin – you want a layer of fat about 5mm deep, and put in the oven for 10 mins until shimmering hot. Carefully tip the potatoes into the hot fat and use a fish slice to turn them until evenly coated. Place in the oven and leave for 40 mins. Remove, turn the potatoes and return to the oven for another 20 mins until golden. Serve sprinkled with the salt.