Thinly slice the scallion separating the white end from the green end.
In a sauce pan on medium high heat, add the butter and melt.
Add the Half & Half, lobster stock reduction and whisk until blended.
Simmer the sauce, whisking until slightly reduced (by about ¼).
Add the basil pesto, lemon juice, sliced white scallion and Parmesan cheese and whisk until thoroughly blended.
Remove from heat, plate, top with green slice scallion and serve.