Preheat the oven to 425 degrees F.
Melt 8 tablespoons butter in a saute pan over medium heat. Add the onions. Season with salt and pepper. Cook for 5 minutes, or until soft, but not browned. Stir in the tarragon and the parsley. Add the seafood. Season with salt and pepper. Cook for 1 minute. Remove from the heat and cool.
With a cleaver or a chef's knife, split the lobsters in half lengthwise. Remove and discard the sac and the intestine. Remove the tomalley and roe, if present and place in a small bowl. Break into small pieces with a fork. With the backside of a knife crack the center of each claw, on one side only. Season the lobsters lightly with salt and pepper. On a baking sheet, place the halves together to resemble a butterfly.
Mix the tomalley and roe into the seafood mixture. Gently fold in the cornbread. Season with salt and pepper. Divide the mixture evenly between the two lobsters. Do not pack the stuffing tightly or it will affect the even baking of the lobster. Brush the 3 tablespoons melted butter over the exposed tail meat, stuffing, and claws. Bake until the lobster is cooked through and the stuffing is crispy and golden, about 20 to 24 minutes. Remove from the oven and serve at once.