Place walnuts in a small skillet over medium-high heat. Stirring often allow walnuts to toast to a golden brown, approximately 2 minutes. Remove from skillet and set aside.

Combine the tarragon, basil, garlic clove and walnuts in the bowl of a food processor. Turn the food processor on and while the ingredients are processing drizzle in the olive oil until all ingredients are pulverized into a pesto.

Taste and add salt and pepper to your preference. Reserve pesto for the chicken.

In a large skillet or casserole (with lid) over medium-high heat, melt the butter. Sprinkle the salt and pepper on the chicken breasts. Lower heat to medium and place the chicken breasts in the pan for 2 ½ minutes (uncovered).

Turn chicken to the opposite side and cook for 3 minutes (uncovered).

Brush or spoon-and-smear the chicken breasts with the pesto on both sides.

Turn off the heat, cover the chicken and allow to sit for 8-10 minutes (if chicken breasts are larger allow to sit 10 minutes).

While chicken is sitting, toss the greens with salad dressing and place serving portions on individual plates (1 1/2 cups per person).

When chicken is complete, slice each breast and place it on a bed of dressed greens. Additional pesto may be added to the chicken breast before slicing if desired. Serve immediately.