Put the butter, two tablespoons of oil, the onions and three-quarters of a teaspoon of salt in a large saute pan for which you have a lid. Turn on the heat to medium, and cook, stirring often, for 16-18 minutes, until soft and deep golden. Transfer half the onions, along with most of the oil and melted butter, to a small bowl and set aside.
Put the split peas, turmeric, 1.2 litres water and three-quarters of a teaspoon of salt in the pan with the remaining onion and bring to a simmer on a medium-high heat. Lower the heat to medium and cook, uncovered, for 20 minutes, then cover with the lid and cook for 35-40 minutes more, or until the split peas are very soft and most of the liquid has evaporated.
Meanwhile, mix all the salsa ingredients in a small bowl.
While the peas are still warm, put them in a blender or food processor with any remaining cooking water, add the last tablespoon of oil and blitz smooth.
Spoon on to a plate, and make a crater in the middle. Stir the reserved buttered onions into the caper salsa, then spoon into the crater. Serve warm or at room temperature with lots of bread for mopping up
