In a large, nonstick frying pan, heat 2 teaspoons of the olive oil over medium heat. Add the shallots and saute until soft and lightly golden, about 6 minutes. Stir in 1/8 teaspoon salt. Transfer to a bowl and set aside.
In the same frying pan, heat the remaining 1 teaspoon olive oil over medium heat. Add the Brussels sprouts and saute until they begin to brown, 3 to 4 minutes. Add the vegetable stock and bring to a simmer. Cook, uncovered, until the Brussels sprouts are tender, 5 to 6 minutes. Return the shallots to the pan. Stir in the lemon zest and juice, the 1/8 teaspoon salt, and the pepper. Serve immediately.