Preheat oven to 450°F (230°C). Cut squash in half and discard the seeds. Place cut side up in a shallow baking dish. In a small bowl, mix butter, maple syrup and brown sugar and then divide between the two cavities. Sprinkle both halves with chili powder, cinnamon, and salt and pepper.
Roast for 45-50 minutes or until flesh is fork-tender. Remove from oven and allow to cool slightly. Scoop flesh into a large bowl and mash together well with a spoon.
Put the egg yolks in a bowl, set the bowl over a pot half full of simmering water. Whisk the yolks for 2-3 minutes until they thicken slightly. Remove the bowl from the heat and begin adding the ghee slowly at first, whisking constantly. Whisk in the lemon juice and season with salt and pepper.
To finish the dish scoop the smashed squash onto the toasted sourdough bread. Top each toast with one poached egg and spoon the hollandaise over the poached egg.