Prepare the Pesto by combining fresh arugula, garlic, nuts, Parmesan, olive oil, and a pinch of salt in a food processor. Blend until smooth.

Soft Boil the Eggs: In a medium pot, bring water to a boil, adding kosher salt and white vinegar. Gently add eggs and boil for 7 minutes.

Prepare the Ice Bath by filling a bowl with ice and cold water. Once eggs are done, transfer them to the ice bath for 5 minutes.

Cook the Polenta: In a saucepan, combine polenta, water, and salt over medium heat. Stir frequently until it thickens, about 20 minutes.

Finish the Polenta by stirring in butter and grated Parmigiano Reggiano until melted and creamy.

Assemble the Dish by spooning polenta into bowls, topping with pesto and peeled soft-boiled eggs, and sprinkling with flaky salt.