How to Make It
Heat a cast-iron skillet over medium-high heat. Cut lemons in half crosswise. Arrange lemons in pan, cut side down; cook 3 to 4 minutes or until cut side of lemon is charred. Remove lemons from pan; cool.
Squeeze 3 charred lemon halves to equal 2 tablespoons lemon juice; cut remaining lemon halves into 6 wedges, and set aside. Combine juice, half-and-half, rind, red pepper, 1 ounce Parmesan, and yolks in a medium bowl, stirring with a whisk. Set aside.
Heat 1 tablespoon oil and butter in a large skillet over medium heat. Add shallot and garlic; cook 30 seconds, stirring constantly. Add mushrooms to pan; cook 4 minutes or until mushrooms release their juices. Remove mixture from pan; keep warm.
Increase heat to medium-high. Add remaining 1 tablespoon oil to pan; swirl to coat. Add shrimp to pan; sprinkle evenly with 1/4 teaspoon salt. Cook 2 minutes. Add wine to pan; cook 2 minutes or until liquid reduces to about 2 tablespoons. Remove pan from heat.
Cook pasta 2 minutes in a large pot of boiling water. Reserve 2 cups pasta cooking liquid; drain pasta. Immediately return pasta to pan over low heat. Add egg yolk mixture to hot pasta, tossing noodles quickly with tongs to coat completely. Stir in mushroom mixture; add pasta water a little at a time (start with 1 cup) to thin sauce to desired consistency. Stir in remaining 3/4 teaspoon salt, basil, and half of shrimp mixture. Divide pasta mixture evenly among 6 plates; top evenly with remaining shrimp mixture. Sprinkle evenly with remaining Parmesan and black pepper. Serve with charred lemon wedges.