To make the fava pureé, add split peas, water, onion, and thyme to a pot over high heat. Partially cover the pot with a lid. Bring to a boil, about 5 minutes, stir, and lower heat to medium-low. Keep the lid partially on the pot and cook for about 30 minutes stirring occasionally and checking for tenderness of the split peas. They should be very soft. Drain through a large strainer or sieve and allow the mixture to drain thoroughly before turning into a pureé
Add the mixture back to the pot and add olive oil, sea salt, and ground pepper to taste. Blend with an immersion blender in the pot until smooth or do this in a food processor. Pour the mixture into your serving dish. Spread out in an even layer, but cool the mixture completely before assembling the remaining components of the dip on top. I used a container with a lid so I placed it in the fridge while I prepared the remaining components.
To make the roasted eggplant, cut the eggplant in half lengthwise. Coat the flesh in a light coating of sea salt and place the eggplant halves on a plate for 30 minutes.
Combine olive oil, smoked paprika, cinnamon, and a pinch of sea salt and ground pepper in a small bowl.
Preheat the oven to 425°F. Then rinse off the salt from the eggplant under water and pat dry with a paper towel. Heat a large cast iron over medium-high heat. Place the eggplant flesh side down in the pan and sear for about 5 to 6 minutes until charred. Brush the skin side with the olive oil mixture, then flip and brush the remaining oil mixture on the flesh side. Keep the eggplant flesh side up and transfer the pan to the oven. Bake for 35 minutes or until softened and totally roasted. Once cooled, about 20 minutes, scoop the eggplant from the skin. It should be very soft, mushy, and easily come off. Roughly chop up the roasted flesh. Now layer this evenly over top of the split pea mixture.
Wipe out the cast iron pan from roasting the eggplant. If it looks too dry add a very small amount of olive oil. Heat over medium-high heat. Add capers and fry until crispy about, 3 to 4 minutes. Remove from the pan and set aside in a small dish.
Layer tomatoes on top of the eggplant, then cucumber, then olives, then feta. Add capers on top and caper leaves if using.
Serve this dip with slices of baguette or toasted pita.