Ina Garten of the Barefoot Contessa makes this mayonnaise. I love it and make it both with and without the cheese. I serve it alongside grilled or poached fish or as a sandwich condiment.

Serves 8

Poached Salmon
1 cup cherry tomatoes, chopped
Basil Parmesan Mayonnaise:
2 extra-large egg yolks, at room temperature
3 tablespoons freshly squeezed lemon juice
1/2 cup freshly grated Parmesan cheese,optional
1 tablespoon Dijon mustard
1/2 cup chopped fresh basil leaves, lightly packed
1/2 teaspoon minced garlic
Kosher salt and freshly ground black pepper
1 cup vegetable oil, at room temperature
1/2 cup good olive oil, at room temperature

Make salmon as per recipe link above.
For the mayonnaise: Place the egg yolks, lemon juice, Parmesan, mustard, basil, garlic, 1 tablespoon salt, and 1 teaspoon pepper in a food processor fitted with the steel blade. Process for 20 seconds, until smooth. Combine the vegetable oil and olive oil in a 2-cup liquid measuring cup. With the processor running, slowly pour the oil mixture through the feed tube to make a thick emulsion. Taste for seasonings — the mayonnaise is a sauce so it should be highly seasoned. Store in the refrigerator until ready to use; it will keep for up to a week.

Serve salmon drizzled with basil mayonnaise and topped with chopped tomatoes.