Rinse one cup of pearl barley in a fine mesh sieve under running water until the water is clear, then transfer to a medium sized pot, along with three cups of water, and boil for 30 minutes or as per the instructions on the packet.
While the barley is cooking, in a round-bottomed wok or pan, heat the olive oil and butter, then add the onion, garlic and grated carrot and fry on low heat until the onion is soft and the garlic fragrant, taking care to brown but not burn the garlic.
Transfer the fried onion, garlic and carrot to your Dutch oven or soup pot, then add the water, sliced carrot, potato, cabbage, and any other wilted vegetables you found in your fridge, along with the seasoning and spices. Turn the heat on to high, bring to a boil, then reduce to simmer on low heat for 20 minutes or so.
When the pearl barley is cooked, add it to the pot, and simmer for another 10 minutes or so. The barley will continue to expand, so add more water if needed, then taste, and adjust the seasoning and spices to suit your palate.
Just before serving, add half a tablespoon of fresh dill to the pot, stir, then distribute between bowls. Sprinkle on the croutons and crispy shallots, garnish with the rest of the dill, and serve with slices of sourdough or toast.