In a small bowl, place red wine vinegar, mustard, olive oil, salt and pepper. Stir with a whisk until well combined, then add beet puree.
Shell and devein shrimp. Slice them on an angle into 4 pieces. In a medium skillet, heat butter and saute carrots, fennel, red pepper, shallots and garlic until vegetables are soft, but not browned. Add shrimp and cook 3 minutes, turning them lightly until they are just opaque. Add the vermouth, cream and tomato paste, then simmer for 4 more minutes. Season to taste with salt and pepper and add parsley. Set aside.
In a mixing bowl, combine the 6 ingredients, blending well. In deep fryer, heat peanut oil until it reaches 350 degrees on a deep-fry-thermometer. Scoop up the mixture with an oval ice cream scoop to form 2-inch oval balls. Carefully place 2 or 3 at a time into the oil. Fry until golden brown, about 2 or 3 minutes. Place on paper towel to drain. When cool enough to handle, cut them in half and with tip of teaspoon carefully scoop out the inside cornmeal to form a hollow shell. Set aside in warm place. Arrange the 3 varieties of lettuce in center of 6 salad plates, and spoon vinaigrette dressing sparingly over them. Warm the shrimp mixture. Arrange 3 halves of the hollowed hushpuppies (per serving) on top of the lettuces. Fill with warm shrimp mixture and sprinkle with chervil. Serve immediately.