Prepare the pesto by blitzing garlic in a food processor for 5 seconds.

Add basil to the garlic and pulse until finely chopped.

Incorporate walnuts, Parmesan cheese, salt, and pepper, pulsing until well combined.

Slowly drizzle in olive oil with the machine running until the pesto reaches a creamy consistency.

Boil sliced potatoes in a large pot with water to cover, cooking for approximately 6 minutes until firm but not fully cooked.

Add green beans to the potatoes and cook for an additional 3 minutes until bright green and slightly crisp.

Drain the vegetables and spread them on a shallow platter.

Toss the vegetables with 1 tablespoon of olive oil.

Incorporate 2/3 cup of pesto, reserving the extra for later use.

Gently toss in the drained tuna fillets, being careful to maintain large chunks.

Taste and adjust seasoning with kosher salt and fresh ground pepper as needed.

Serve with additional grated Parmesan cheese at the table.