Preheat your oven to 425 degrees. Cut your fennel in half legthwise. Remove the core from each half (the tough part at the root end) then give the fennel a rough dice. Cut your shallot into a rough dice also. Put the diced fennel and shallot on a baking tray and drizzle with 1 tablespoon of olive oil. Sprinkle everything with a pinch of salt then toss to coat. Roast the fennel and shallot at 425 for about 25-30 min or until caramelized around the edges and tender. Remove from the oven and set aside.

While the fennel and shallots are roasting, dice the potatoes into 1-inch cubes (this will be roughly 2 1/2 to 3 cups total).  Add the diced potatoes to a large stock pot. Cut away the rough skin of the celeriac then cut it into a rough 1-inch cubes as well. Add the celeriac to the pot with the potatoes, then cover the vegetables with cool water. The level of water should be at least an inch above the vegetables. Set the pot on a burner over medium high heat. Bring everything to a boil, then boil for about 12-15 minutes or until the potatoes and celeriac are fork-tender. Strain and rinse the cooked potatoes and celeriac under cool water. 

Add the coconut milk, roasted fennel and shallot, vegetable bouillon cube, and the nutritional yeast to a blender. Blend on high until smooth. Add potatoes and celeriac and pulse a few times to incorporate them into the soup. You want to pulse instead of blending so that you keep the potato starches from developing (which will yield a weird gluey texture).

Add the soup back to the stock pot and warm it to your liking. Give it a taste and season with salt as needed.

While the soup warms, make the smoky shiitakes. Remove and discard/compost the stems of the mushrooms then cut them into slices roughly 1/4-inch thick. Add 1 tablespoon of the oil to large skillet set over medium heat. Add the sliced mushrooms along with the granulated garlic, smoked paprika, and tamari or soy sauce. Stir to combine, then allow the mushrooms to cook, stirring occasionally, until the mushrooms are golden brown. This will take about 5-7 minutes.

To serve, top each bowl of soup with some of the smoky shiitakes. You can also garnish with some of the fennel fronds if you like or some shredded vegan or regular cheddar cheese.