Wash and clean the potatoes.
Put the potatoes in a pot and fully cover them with cold water (with the water line about 1 inch above the potatoes) and add salt to the water (about 1/2 tsp regular salt).
Bring the potatoes to a boil over medium-high heat (it will take about 10 minutes) and then lower the heat so the potatoes simmer until they’re cooked through (soft when pierced with a knife). It will take about 20-25 minutes, depending on the size of the potatoes. Drain the potatoes.
Return the pot to the stove on medium heat and add the unsalted butter. Once the butter has melted, add the Italian dried herb seasoning (or dried oregano), minced garlic, lemon zest, salt, and pepper. Sauté for about 30 seconds.
Add the drained potatoes and the lemon juice to the pot and keep cooking while stirring for about 1-2 minutes until the potatoes are coated in the sauce. Turn the heat off and leave the potatoes in the pot for about 2 minutes.
Add the finely chopped fresh basil to the potatoes and stir with a heatproof silicone spatula until the sauce and basil evenly coat the potatoes. Transfer to a bowl and serve.