Over medium-high heat, toast the pine nuts in a dry skillet (do not add oil), stirring frequently, so they don't burn. This process should take about 5 minutes, and they should be golden and fragrant. Set aside.
Prepare beans by washing and trimming the ends and then cutting to the desired length.
Bring a large pot of water to a boil. Add beans, return to boil, and simmer until crisp-tender, 3 to 4 minutes (less time for crunchier beans). Drain the beans and, rinse with cold water, set aside.
Heat ½ teaspoon oil in a large skillet over medium heat. Add prosciutto; cook until crispy, 4 to 5 minutes. Drain on a paper towel-lined plate.
Using the same pan you cooked the prosciutto in (pour out any excess oil from the prosciutto), heat the remaining 2 teaspoons of oil over medium heat. Add the beans, garlic, sage, salt, and several grinds of pepper. Cook, stirring occasionally until the beans are brown in places, 3 to 4 minutes.
Plate the beans and sprinkle with prosciutto and pine nuts. Season as needed with additional salt and pepper.