Preheat oven to 425 degrees.
On a large baking sheet, toss together the apple, carrot, onion, garlic, rosemary,1 tablespoon extra virgin olive oil, and a big pinch each of salt and pepper. Spread the ingredients in a single layer (as best you can). Dot various spots with the butter.
Roast for 20 minutes, tossing the goodies once halfway through, until tender and fragrant. Remove and let cool slightly.
Add the sheet pan components to a large food processor or high speed blender along with the pumpkin, smoked paprika, and maple syrup. Puree until smooth, scraping down the sides of the bowl as needed to reincorporate the ingredients. Taste and adjust seasonings as needed.
In the meantime, heat the broth in a large soup pot over medium heat. Scoop in the pureed soup and pour in the coconut milk. Stir for 5-10 minutes to heat through.
If desired: use a fine mesh sieve to scoop out heaps of soup and carefully strain back into the pot, shaking the sieve to separate the fibrous solids. This will make your soup extra creamy!
Ladle into bowls and top with a swirl of cream and crispy rosemary. Serve with crusty bread!