In a medium, deep ovenproof skillet, heat 2 tablespoons of the olive oil until shimmering. Add the carrot mixture and a generous pinch of salt and cook over moderate heat, stirring occasionally, until softened slightly and nearly dry, 5 to 7 minutes. Add the tomato puree and cook, stirring occasionally, until most of the liquid has evaporated, 5 minutes. Stir in the remaining 6 tablespoons of olive oil. Transfer the skillet to the oven and bake for 1 1/2 hours until the carrot sofrito is very soft. Season with salt, cover and keep warm over low heat, stirring occasionally.