Bring a large pot of water to a boil. Add beans, return to a boil, and simmer until crisp-tender, 3 to 4 minutes. Drain.
Heat 1/2 teaspoon oil in a large nonstick skillet over medium heat. Add prosciutto; cook, stirring, until crispy, 4 to 5 minutes. Drain on a paper towel.
Wipe out the pan; heat the remaining 2 teaspoons oil over medium heat. Add the beans, garlic, sage, 1/8 teaspoon salt and several grinds of pepper. Cook, stirring occasionally, until the beans are browned in places, 3 to 4 minutes. Stir in pine nuts, lemon zest and the prosciutto. Season with lemon juice, the remaining 1/8 teaspoon salt and pepper.