I added a dollop of yogurt to a bowl. Helped some, but not enough for picky guests!
The best thing to do is a bit more work, but worth saving a whole batch... Cook more carrots completely unseasoned. Puree those and add. Coconut milk might also help, or unsalted butter - depending on what the previous ingredients are. A desperate measure might be to cook & puree potatoes too - they're sort of "blank canvas" tasting...
Agree that adding more pureed cooked carrots is going to come closest to the desired result. I had to do this once with butternut squash soup (too much red curry - won't make that mistake again!) - cooked a second squash to add to the soup and it was perfect.
Stirring in some coconut milk would help to blunt the edges of the spice a little bit. Diluting it significantly would of course help, particularly if it's not just with liquid. It sounds like it's a pureed soup; do you have anything already cooked that would taste good blended in? I think squash, sweet potatoes, potatoes, or rice would work.
I'm not familiar with coconut milk, so I'd lean towards sour cream
Here's an option depending on how adventurous you are
Knowing that the opposite of spicy is sweet and looking at flavors that pair well with carrots the recommended sweet items are: Maple Syrup, brown sugar, orange juice, honey and apple juice (best profiles listed first). Taking a look at maple syrup you'll find orange juice and carrots as suitable flavor matches, I'd take a run at making a Spicy Carrot, Maple and Orange soup leaving the spicy carrot the primary flavor with the others as accent flavors.
If you decide not to do this, send me the carrot soup recipe (as written) and I'll try this, just because it sounds fun and I'm willing to put my money where my taste buds used to reside
I had similar experiences.... Adding buttermilk could help. Or you can add a ton of it and evolve the soup into a curried carrot smoothie :)
I, too, use coconut milk. The full fat one is best. Also try adding a cooling herb such as cilantro or parsley.
Sounds like you're looking for a dilution solution. Meaning: thin it out with something, whether it's coconut milk or stock.
Depending on whether recipe is freezable, divide into small portions and freeze, considering it a concentrate. Then defrost each when you need a new batch of soup and experiment in smaller quantities with one or more of the suggestions here.