In a Dutch oven or large stockpot set over medium heat, melt the butter. Introduce the diced onion, sliced carrots, and celery, cooking them with occasional stirring until they soften, approximately 3 to 4 minutes. Add the minced garlic and Italian seasoning, continuing to cook until aromatic, about 1 minute.
Incorporate the flour by whisking it in until it begins to take on a light golden hue, around 1 minute. Pour in the white wine, deglazing the pan by scraping up any browned fragments from the bottom.
Gradually stir in the chicken stock along with the bay leaf, seasoning to taste with salt and pepper. Bring the mixture to a boil, then reduce the heat to low, cover, and allow it to simmer gently for about 10 minutes to meld the flavors.
Add the shredded rotisserie chicken and tortellini, cooking until the pasta is tender, roughly 4 to 5 minutes.
Blend in the heavy cream, frozen peas, lemon juice, and chopped parsley, stirring until the soup is thoroughly heated, about 2 minutes more. Adjust seasoning with additional salt and pepper if necessary.
Serve hot and enjoy immediately.