Heat the olive oil in a pot over medium heat. Add the chopped onion and carrots and sauté until softened.
Add the water, yellow split peas, and salt.
Lower the heat and simmer until the split peas have completely broken down and the mixture has thickened.
Remove the pot from the heat.
Use a hand blender to blend the fava until smooth and creamy.
The finished fava should be thick, creamy, and smooth. If it seems too thin, continue cooking for a little longer to allow some of the excess liquid to evaporate.
Char the Leeks
Cut the leeks into pieces approximately 2.25 in long.
Grill the leeks until the outer layer is deeply charred.
Place the grilled leeks in a baking dish with a small amount of water and seal tightly.
Bake for approximately 20 minutes, or until the centers are completely tender.
Remove the charred outer layer from the leeks, keeping the tender centers.
This two-step cooking process is what gives the leeks their incredible texture—the outside gets smoky and charred while the inside becomes soft and sweet.
Assemble and Serve
Spoon the fava onto a serving plate or shallow bowl.