Bring 4 quarts of water to a boil. Add the cubed squash and cook for 5 minutes, or until just tender when pierced with a knife. Drain.
In a large skillet, add the olive oil and bring the temperature to medium heat. Add the sage leaves and cook until just crispy, about 5 minutes. Add the butternut squash and season with sea salt. Add the balsamic and cook about 1 minute.
Remove from heat and place on toasted crostini. Top with grated Parmigiano.