Heat the vegetable oil in a large Dutch oven over medium heat until it shimmers. Add the wheat berries and cook, stirring frequently, until they are toasted and smell nutty, about 5 minutes.

Add the onions and cook until they are softened and translucent, about 5 to 7 minutes. Stir in the garlic, thyme, tomato paste, and cayenne, and cook until the tomato paste darkens in color and the mixture is fragrant.

Pour in the vegetable broth and water, scraping any browned bits from the bottom of the pot. Bring the liquid to a boil, then reduce the heat to low, cover, and simmer until the wheat berries are starting to soften, about 45 minutes.

Stir in the shredded cabbage, beets, carrot, and bay leaf. Continue to simmer, covered, until both the vegetables and the wheat berries are completely tender, 30 to 40 minutes.

While the soup finishes, whisk the sour cream, dill, and salt together in a small bowl until smooth.

Remove the bay leaf and stir in the red wine vinegar. Season the soup with salt and pepper to taste, and serve hot with a dollop of dill cream.