My grandmother makes a soup called Chicken Pastina soup that uses an alternative egg method. Here are the ingredients.
Using the Pastina, Chicken, and broth, make a normal chicken soup (as you usually might with regular chicken soup) and scramble the eggs in a seperate pan.
Add the scrambled egg into the hot ...
I would sweat one of each of the vegetables (chopped) in 4tsp oil, beginning with the onion, leek, carrot, celery, and 2 sliced garlic cloves. Then add a TBS of tomato paste. Add zucchini and sweet potato, one each, chopped, Cook for a minute or two. Add 1/4 tsp black pepper and red pepper. Add 1/2 tsp thyme. Toss in one roasted red pepper, chopped, ...
Note: This is a suggested experiment, rather than a tried-and-tested solution
From the comments, yeast and malt extracts were suggested. I'd go further and say both, as neither will replicate beer flavour alone.
Both are rather variable. Some experimenting will be required.
In case you go too far with either of them, I suggest you have spare ingredients on ...