In a medium pot, melt the butter and oil. Since this borscht is vegetarian, this is your source of fat and additional flavor.
Add the onion and carrot. Saute until the veggies are soft for about 7 to 9 minutes. Then add diced tomato and cook for another 2 minutes.
Now it's time to add water (you can also use vegetable stock). With liquid, it's always a bit tricky because the amount will never be the same. It will depend on how big is your pot, and how much vegetables you're using. For me, it's usually about 12 to 14 cups, but I never measure the exact amount. Just use your common sense, and you'll be fine.
Add the beets, potatoes, and dried bay leaves to the pot and bring to a boil. Add a good pinch of salt to taste. Lower the heat to medium-low and continue cooking for another 15 minutes. You're looking for a slow simmering, not an intense boiling.
Add the shredded cabbage. Cook the borscht for another 10 to 15 minutes until the vegetables are soft. Add the minced garlic, chopped herbs, and season to taste with salt and pepper. Continue cooking for 2 more minutes.
Serve the borscht hot, preferably with a dollop of sour cream.