Heat the oven to 220 C / 425 F. Toss the squash cubes and onion wedges on a 33 x 46 cm / 13 x 18-inch sheet pan with 3 tbsp olive oil, 1/2 tsp of the salt and the black pepper. Spread everything in a single layer with space between the pieces so it browns instead of steams.
Roast for 35 minutes, flipping the pieces once at the 20-minute mark, until the edges are browned and a knife slides into the squash with no resistance.
Heat the remaining 1 tbsp olive oil in a 5-quart / 4.7 L pot over medium heat. Add the garlic, ginger, 12 chopped sage leaves and turmeric. Stir for 30 to 45 seconds until fragrant.
Add the roasted squash and onion, the broth and the remaining 1/2 tsp salt. Scrape any browned bits from the sheet pan into the pot with a splash of broth. Bring to a boil, then reduce the heat and simmer uncovered for 10 minutes.
While the soup simmers, heat 1 tbsp olive oil in a 20 cm / 8-inch skillet over medium heat. Fry the 8 whole sage leaves for 30 to 45 seconds until crisp, then lift them onto a paper towel.
Stir the coconut milk and lemon juice into the pot. Blend with an immersion blender for 1 to 2 minutes until completely smooth. For a countertop blender, work in batches, fill it no more than halfway and vent the lid. Thin with hot broth or water if needed, then taste and add salt.
Ladle into bowls and top with the crispy sage and a crack of black pepper.