Place the potatoes, chicken stock, lemon juice, 2 tablespoons olive oil, 1 teaspoon salt, and 1/4 teaspoon black pepper in a medium saucepan. Bring to a boil over medium-high heat. Reduce the heat and simmer until the potatoes are tender, about 20 to 25 minutes.
Drain the potatoes and place in a serving bowl. Drizzle with the remaining olive oil. Add the lemon zest and 3 tablespoons of the basil. Toss well and garnish with the remaining chopped basil.