Combine 1 tablespoon of salt and water in a stock pot along with cubed potatoes. Bring to a boil. Once water is boiling, cook until the potatoes are tender, about 5 minutes.
Drain water, and spread potatoes onto a parchment lined baking sheet. Place the baking sheet into the refrigerator for 30 minutes, or until the potatoes are completely chilled.
Meanwhile, cook the pancetta in a skillet over medium heat until browned and crisp, stirring occasionally. This should take about 8 minutes. Remove pancetta from the skillet and place on a towel to cool and absorb excess oil.
In a small bowl, combine mayonnaise, lemon juice, and sea salt. Use a spatula to fold ingredients together until well combined to create an aioli.
Make the dairy free parmesan cheese by placing cashews, nutritional yeast, and ¼ teaspoon sea salt in a food processor, and pulse until it forms a fine meal. Fold into the aioli, and set aside.
Place potatoes in a medium bowl; gently fold in pancetta, aïoli, and hard-cooked eggs. Top with basil just before serving. Serve chilled.
Bacon can be substituted for pancetta.
The dairy free parmesan cheese can be replaced with ⅓ cup parmesan cheese if tolerated and not following Whole30.
If you cannot tolerate eggs, you can omit the hard boiled eggs and replace the mayo with this recipe.