To Make the Pesto

Toast the walnuts in a dry pan over a medium heat until fragrant and golden brown, stirring frequently, about 3 minutes.

In a food processor, process the walnuts and the garlic until minced.

Add the basil, Parmesan cheese and lemon juice and process until finely minced. With processor on, slowly pour the oil down the food chute.

Process until well blended. Season with salt and pepper, to taste.

To Make the Parmesan Walnuts

Add all ingredients to a skillet and cook on medium heat until the butter and Parmesan have melted and the mixture is just starting to turn brown. Turn out of the skillet onto a piece of foil to cool. Separate if necessary.

To Make the Potato Salad

Cook the potatoes in boiling water for 20 minutes until fork tender.

Quarter the potatoes and put them in a large bowl with the onions. Add the pesto and toss gently to combine; let sit for at least 30 minutes.

Add the olive oil and stir gently; season with salt and pepper to taste.

Add 1 cup of the Parmesan walnuts and toss; garnish with the remainder of the nuts.

Serve at room temperature.