In a large stockpot, heat 2 tablespoons of extra-virgin olive oil over medium heat. Once shimmering, add 1 medium diced yellow onion and 2 medium carrots, chopped. Sauté for about 5 minutes until the onions are softened and translucent.

Stir in 3 minced garlic cloves and cook for another minute, allowing the garlic to release its fragrant aroma.

Next, add 4 tablespoons of unsalted butter to the pot. Once melted, sprinkle in ¼ cup of all-purpose flour, whisking continuously. Cook this mixture for about a minute until it forms a thick paste.

Gradually pour in 6 cups of chicken stock, whisking to break up any lumps in the roux. Increase the heat to bring the soup to a gentle boil.

Stir in 1 teaspoon of kosher salt, ¼ teaspoon of black pepper, ¾ cup of long-grain white rice, and 4 cups of roughly chopped green cabbage. Allow the mixture to simmer on low for about 20 minutes.

After the rice is tender, reduce the heat and gently stir in 1 cup of whole milk, ¼ cup of chopped fresh dill, and the juice of ¼ cup plus 2 tablespoons of fresh lemon.

Finally, fold in 3-4 cups of coarsely shredded rotisserie chicken. Simmer the soup for another 5 minutes until heated through.

Ladle the warm soup into bowls, and garnish with additional dill and a sprinkle of black pepper if desired.