I haven't made this soup, but I make soups and sauces from scratch all the time. The reason many people complain of "grainy" texture is the shredded cheese. Pre packaged shredded cheese contains starches and other ingredients that create that gross texture. I always chop a full bar of cheese to add to my meals. It doesn't have to be expensive. Makes all the difference! Also, add slowly. 2oz at a time max, and stir until it blends. Then add a little more until it's all in there.
That said, I am surprised this soup is thick without a roux but besides that, it looks very similar to my own recipe and my family always loves it.
I added carrots, 3 medium size potatoes, cauliflower and some cumin. Added extra cup of water and it was still very thick soup. Tasted great but it was a little grainy. Next time I'll process raw veggies (before cooking) because when I do that for my spinach and broccoli cream soup it's not grainy at all. Overall great tasting and very easy to make. Took me about half an hour from start to finish.
I doubled the recipe and used more garlic cloves than the recipe suggested (so doubling I used a total of 6 garlic cloves, would only add one extra for a total of 3 if making the recipe as is). Because it was such a big batch I used an immersion blender, which left a little of it a bit chunky... it actually made it way easier and I liked it a lot! That's how I'd do it even if were the single batch. It was sooooo good.