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In a large saucepan, heat 2 tablespoons of the oil. When the oil is hot, add the onions. Season with salt and pepper. Saute for 2 minutes. Add the crushed red pepper, garlic, and split peas. Continue to saute for 1 minute. Stir in the water. Bring the liquid to a boil. Reduce the heat to medium-low and simmer until the peas are tender, about 1 1/2 hours.
In a small mixing bowl, toss the fennel with the remaining 1 tablespoon of olive oil. Season with salt and pepper. Place on a parchment lined baking sheet and place in the oven. Roast for about 25 minutes, or until golden brown. Remove from the oven and cool completely.
In another mixing bowl, toss the lobster, fennel, red onion, and extra-virgin olive oil. Season with salt and pepper. Using a hand held blender, puree the soup until smooth. Stir in the milk. Season with hot sauce, salt and pepper. To serve, ladle the soup into the individual bowls. Spoon the salad in the center of each bowl. Garnish with fried parsley.