Preheat the oven to 425°F. Place the honeynut squash halves on a sheet pan. Drizzle with olive oil, rub to coat, and season with a good pinch of salt. Arrange the squash cut-side down. Roast for 40 minutes, or until tender. Allow the squash to cool to room temperature.
Scoop out the squash and discard the skins. Add the squash to a food processor, along with the feta, a ¼ cup of olive oil, and 1 tablespoon of honey. Pulse to combine. With the food processor running, slowly drizzle in the water, blending until smooth.
Heat a 12” stainless steel skillet over medium heat. Add the remaining ¼ cup of olive oil. Once hot, fry the sage leaves in the oil for a minute or two until crisp. Use a slotted spoon to transfer the sage to a paper towel.
Reduce the heat to medium-low and add the sliced chile peppers to the oil. Cook for a minute or two until softened. Add the pecans and toast for a few seconds until fragrant. Stir in the remaining 2 tablespoons of honey. Allow the mixture to simmer for about a minute until thickened. Turn off the heat.
Spoon the dip into a shallow serving bowl. Top with freshly cracked black pepper. Spoon the honey pecan topping over top and garnish with the fried sage leaves. Serve with toasted bread or crackers alongside for dipping.