Preheat oven to 400 degrees. Drizzle cut sides of squash with oil and season with salt. Arrange cut side down on a baking sheet. Arrange garlic head halves in the center of parchment-lined foil. Drizzle with oil, sandwich, and wrap tightly. Transfer to baking sheet with squash and roast until squash and garlic are tender, about 45 minutes.

When cool enough to handle, scoop squash flesh and squeeze each clove of roasted garlic. Transfer to a food processor with oil, lemon juice, tahini, and turmeric and process until smooth. Season with salt and cayenne. Store dip in an airtight container up to five days.