Preheat oven to 375 degrees Fahrenheit (190 degrees Celsius).

Blend all pesto ingredients. Smear two tablespoons of the sauce over the salmon pieces.

Add 1/4 cup mayo and 1/4 cup olive oil to the remaining pesto and set aside for the dipping sauce.

Smear phyllo sheets with olive oil and stack one on top of another. Cut into 1/2-inch (1 and 1/4 centimeter) strips. Twist a stack of strips around each salmon slice.

Lay the salmon slices on a lined baking sheet. Place in oven and bake for 10 minutes. Raise oven heat to broil and broil for one to two minutes.

Thread two wrapped salmon fingers on each skewer and serve alongside the dipping sauce. Alternatively, make the same recipe using both salmon and sea bass, and thread one salmon finger and one sea bass finger on each skewer. For sea bass, add three sundried tomatoes to the dipping sauce.