How to Make It
To prepare peas, heat a large skillet over medium-high heat. Add oil to pan. Add chopped onion and salt; sauté 5 minutes or just until tender. Place split peas in a large Dutch oven. Add sautéed onion and its oil; cover pea mixture with water by 4 inches. Bring to a boil; reduce heat to low, and simmer, skimming frequently, 5 minutes. Add turmeric and bay leaves; simmer 30 minutes or until peas are soft and almost dry, stirring occasionally. (Add warm water, if needed, to keep the peas covered as they cook.) The peas are done when they are very soft and almost dry. Remove bay leaves; discard. Place pea mixture in a food processor; process until smooth. Place puree in a large bowl; cool completely.
To prepare caper relish, place salt-packed capers in a colander; rinse under lukewarm running water for 2 minutes or until they lose excessive saltiness. Drain capers well; pat dry with paper towels.
Heat a large skillet over medium heat. Add 1/4 cup oil. Add pearl and red onions; cook 8 minutes, stirring occasionally. Add capers, chopped chicory, and remaining 1/4 cup oil; cook 4 minutes or until greens are wilted, stirring occasionally. Stir in wine; cook 1 minute. Stir in 1/2 cup water; reduce heat to low, and cook 8 minutes. Increase heat to high, and cook 16 minutes or until liquid evaporates and onions start to caramelize, stirring occasionally. Remove pan from heat; stir in vinegar and pepper.
Place pea puree in a shallow bowl, using a spoon to create a well in the center. Place caper relish in well.