Melt butter over medium heat in a large Dutch oven.
Add onion, celery, and carrots and cook until soft, about 5 minutes.
Add garlic and cook 1 more minute.
Sprinkle flour over cooked veggies and stir and cook for 1 minute.
Gradually whisk in the chicken broth. Add bay leaf, black pepper, chicken bouillon, and ham and bring to a simmer.
Simmer for 20 minutes. Add white beans, parsley, and half-and-half.
When mixture returns to a simmer, add tortellini. Cook for 2 minutes. Remove from heat and serve.