Heat olive oil in a large sauce pan or Dutch oven over medium, Whisk in flour continuously until fully combined with oil. Stir in onion, carrot, and celery and cook until soft, about 5-8 minutes. Mix in garlic, stir for one minute, then add turmeric, paprika, sage, cinnamon, tomato paste, and honey and warm an additional minute or two. Pour in broth or water and butternut squash cubes. Bring to a boil, then lower to a simmer and cook for about 8-10 minutes until squash is very soft and falls apart when pierced with a fork.
Here you have two options. The first, my preferred, is to cream everything with an immersion blender until smooth and completely blended. I find this much safer, more efficient, and less messy than the following second option: a traditional blender. If that is your tool of choice, transfer 1-2 cups at a time and blend carefully until creamy, repeating batches until all of the soup is done. Once soup is back in the pot, pour in milk and season with salt and pepper to taste.
During the squash boiling phase, prepare your gnocchi according to package directions. Alternatively, you can simmer the gnocchi directly in the soup if you want, but I find it takes on a strange doughy texture that way.
Make the crostini. Heat broiler to HIGH. Melt butter in the microwave for :30, when whisk in garlic and a touch of salt and pepper to taste. Spread crostini rounds onto a baking sheet and brush one side with butter. Place under the broiler for 2-3 minutes until golden. Remove from oven, flip each crostini so the toasted side faces down, and brush the tops with remaining garlic butter. Sprinkle with asiago. Slide under the broiler once more for an additional 2-3 minutes until cheese melts, bubbles, and turns a light golden brown in spots.