Preheat the oven to 375°F. Line a baking sheet with parchment paper.

Carefully cut the butternut squash in half lengthwise. Scoop out the seeds and stringy bits.

Brush inside the squash all over with the oil. Season with salt and pepper. Place the squash halves, cut side down, on the baking sheet. Bake for 45-60 minutes, depending on the size of your squash, until fork tender.

In a large skillet, heat the oil over medium-high. Once it's hot, add a few sage leaves at a time. Fry them a few seconds per side, allowing the oil to drip off as you lift them from the skillet and place on a plate lined with paper towel. The sage leaves will lose their softness and crisp almost immediately upon cooling. If they don't, fry them a bit longer. Fry the rest of the sage in batches. Reserve 1 tablespoon of the fried sage leaves (minced) for the stuffing. The rest can be used as garnish.

Reduce the heat to medium-low. Sauté the shallot in the sage-infused olive oil until soft, 2-3 minutes. Add the garlic, sauté for 30 seconds, then add the remaining ingredients (except the apple cider vinegar) including the reserved minced fried sage. Cook until the apples are slightly softened but not mushy, about 6-10 minutes, stirring often and scraping the bottom of the skillet to prevent burning. Stir in the apple cider vinegar. Taste, then season and add more minced fried sage, if desired.

Divide the stuffing between the two squash halves. Garnish with remaining sage leaves. Serve immediately.