If I'm going to put a vegetable in a soup, chances are very high that I'm going to roast it first. Roasting is great for bringing out flavors and sugars. I'd really recommend it. Plus it pre-cooks vegetables which makes soup-making go faster.
To make "Loaded Baked Potato Soup" I roasted 4 Russet Potatoes in olive oil and salt. They come out looking like giant french fries. Delicious.
Then put the potatoes in a soup pot with no oil. You already have oil on the potatoes. I'm not sautéing onions because I'm putting green onions in later to give it that baked potato feel. IF you need onion, and since there is no oil in the soup pot I would say go ahead and roast the onions with the potatoes so you don't need to saute them.
Add whatever dairy free milk you'd like, or whichever you have. I had a bit of almond milk left and then used soy for most of it. Bring it to a simmer. It doesn't need to boil since the potatoes are already cooked and ready to go.
Add a tiny splish of liquid smoke. This will simulate the bacon flavor. Add a little, you can always add more but not take it out. I like it as a background flavor. You don't want it to taste like BBQ Potato Soup.
I used an immersion blender, you could transfer the soup to a blender if you find that easier. I don't, I like using one pot for everything so an immersion blender is my favorite thing ever. I use it for smoothies.
Blend the soup until mostly smooth, leave a few chunks if you so please.
I dissolved a (vegan) bouillon cube into some water and added water until it was a texture I liked, after blending it looked more like mashed potatoes than potato soup.
Then add some Cheddar Daiya. I didn't measure, I put 2-3 handfuls in the pot. Stir until it melts. Save some sprinkles for the top because it's pretty. It melts really well and got creamier than I expected. Bonus!
Green onions are next, Mix some in and sprinkle them on the top. Plus salt and pepper to taste. I would probably skip the salt though, since it was already on the potatoes. We will call it, peppering to taste :)
I put mine in Tupperware to eat for lunch the next day. When I re-heated I had to add more water since it thickens up. I served it with a pretty basic garden salad of romaine, tomatoes, broccoli, corn, celery, and carrots.