To make the fava, rinse split peas in plenty of water. Heat a large saucepan over a medium high heat, add 2 Tbsp of the olive oil, chopped onion, garlic, thyme and oregano and sauté.
As soon as the onions start to caramelize, add tomato paste and cook 5 minutes, then add split peas and bay leaves and stir. Pour in the warm stock, turn heat down to medium, and season well with salt and pepper. Simmer with the lid on 40 to 50 minutes until split peas are thick and mushy. While split peas are boiling, white foam will probably surface on the water—remove this with a slotted spoon.
Meanwhile, for the griddled vegetables, heat up a griddle/grill pan and lightly brush with olive oil. Season the lettuce and radicchio with salt and pepper and griddle on each side until slightly charred and soft but still with bite.
Pour lemon juice into the pan of split peas, add paprika and chile/red pepper flakes, and transfer mixture into a food processor—or alternatively, if you prefer a coarser texture, don’t process. Mix until peas become smooth and creamy, like a purée.
Serve the fava with remaining olive oil drizzled over, and with the griddled vegetables, sliced onions, capers and crusty bread.