In a large pot, drizzle olive oil over medium heat. Add the shallots and cook, stirring often, until softened. Stir in the garlic and cook until just fragrant, 30 seconds to 1 minute.
Add the pumpkin and continue to cook for a minute before pouring in the vegetable stock and milk. Bring the mixture to a boil, then decrease heat to a simmer. Cook, stirring occasionally, for 30 minutes. Remove from heat and stir in the shredded Garlic Basil Cheese until melted and combined. Season with salt to taste.
Divide the soup among serving bowls or hollowed out, roasted pumpkins. Top with Garlic Basil Cheddar Crisps, croutons, and toasted sesame seeds. Serve immediately.