Lobster Crisps in Champagne-Dill Sauce

Preparation Preheat oven to 350°F. Melt 1 tablespoon butter in small saucepan. Brush gyoza on both sides with butter. Arrange on baking sheet. Bake until golden, about 8 minutes. Cool; wrap crisps airtight. Cook lobster in large pot of boiling salted water until just cooked through, about 8 minutes. Transfer lobster to large bowl. Let stand 15 minutes. Working over bowl to catch juices, twist lobster tails and claws from body. Crack shells and carefully remove lobster meat. Cover and refrigerate lobster meat. Place all lobster shells and juices in large saucepan. Add Champagne, 2 cups water, shallots and tomato paste. Simmer until liquid is reduced to 1 cup, about 1 hour. Strain liquid; return to same pan. Add cream; simmer until sauce is reduced to 1/3 cup, about 6 minutes. (Crisps, lobster and sauce can be prepared 1 day ahead. Store crisps at room temperature. Cover and refrigerate sauce.) Melt 2 tablespoons butter in heavy large skillet over medium-low heat. Add fennel and carrots; sauté 3 minutes. Add leek and sauté until vegetables are crisp-tender, about 2 minutes. Cut lobster tail crosswise into 8 medallions. Add all lobster to skillet. Cover; cook just until heated through, about 2 minutes. Mix in 2 teaspoons dill. Season with salt and pepper. Rewarm sauce over low heat. Whisk in 2 tablespoons butter and 2 teaspoons dill. Season with salt and pepper. Arrange crisps, lobster, and vegetable mixture on 2 plates. Spoon sauce over.

Preparation Preheat oven to 350°F. Melt 1 tablespoon butter in small saucepan. Brush gyoza on both sides with butter. Arrange on baking sheet. Bake until golden, about 8 minutes. Cool; wrap crisps airtight. Cook lobster in large pot of boiling salted water until just cooked through, about 8 minutes. Transfer lobster to large bowl. Let stand 15 minutes. Working over bowl to catch juices, twist lobster tails and claws from body. Crack shells and carefully remove lobster meat. Cover and refrigerate lobster meat. Place all lobster shells and juices in large saucepan. Add Champagne, 2 cups water, shallots and tomato paste. Simmer until liquid is reduced to 1 cup, about 1 hour. Strain liquid; return to same pan. Add cream; simmer until sauce is reduced to 1/3 cup, about 6 minutes. (Crisps, lobster and sauce can be prepared 1 day ahead. Store crisps at room temperature. Cover and refrigerate sauce.) Melt 2 tablespoons butter in heavy large skillet over medium-low heat. Add fennel and carrots; sauté 3 minutes. Add leek and sauté until vegetables are crisp-tender, about 2 minutes. Cut lobster tail crosswise into 8 medallions. Add all lobster to skillet. Cover; cook just until heated through, about 2 minutes. Mix in 2 teaspoons dill. Season with salt and pepper. Rewarm sauce over low heat. Whisk in 2 tablespoons butter and 2 teaspoons dill. Season with salt and pepper. Arrange crisps, lobster, and vegetable mixture on 2 plates. Spoon sauce over.