Spread the black eyed peas on a large baking sheet and pic over to remove any damaged peas or debris. Put peas in a large pot, add enough water to submerge by 2 inches, and bring to boil over high heat. Boil 1 minute. Set aside, off the heat and soak for an hour. Drain in a colander set in the sink.
Warm 1/8 cup oil in a large pot or Dutch Oven set over medium heat. Add the onion and fennel. Cook, stirring often, until soft, about 8 minutes. Add garlic and cook until fragrant, about 20 seconds. Stir in black eyed peas, carrots, tomato, tomato paste, bay leaves, and salt until tomato paste dissolves. Add enough water just to cover the vegetables. Raise the heat to medium high and bring to boil.
Cover, reduce the heat to low, and simmer slowly until the black eyed peas are tender about 50 minutes.
Stir in the kale leaves and dill. Cover and cook until kale is tender, 5-10 minutes. Discard ant bay leaves. Ladle into two bowls. Drizzle 1/2 tbsp olive oil on top of each serving.
TIP: For quicker meal, substitute frozen black eyed peas, thawed.