Step 1Cook the pasta: In a large bowl of salted boiling water, add the pasta. Cook until al dente according to the package instructions. Drain the pasta.
Step 2While the pasta is cooking, start to make the sauce: In a medium saute pan, melt the butter over medium heat. Add the basil and cook, stirring frequently, until aromatic, about 3 minutes. Stir in the lemon juice and continue to cook until the lemon juice is reduced by half. Reduce the heat to low and add the cream. Slowly cook the cream until it thickens to a sauce consistency, stirring occasionally, about 5 minutes. Remove from heat.
Step 3Divide the pasta among 4 to 6 serving bowls and ladle the sauce evenly over the servings. Divide the cheese among the portions, sprinkling it evenly over the sauce, and top each serving with a few grinds of black pepper. Serve each portion with a lemon wedge on the side.