In a large saucepan, heat olive oil over medium-high heat. Add diced onions, chopped carrots, and sliced celery. Sauté for 5-7 minutes until vegetables soften and onions become translucent.

Once the vegetables are tender, stir in minced garlic, fresh thyme, and optional red pepper flakes. Cook for 1 minute until fragrant.

Pour in chicken or vegetable broth, adding the canned white beans and chopped fresh rosemary. Bring to a boil, then reduce heat to low and simmer uncovered for 10 minutes.

Turn off the heat and stir in grated Parmigiano Reggiano cheese until melted.

Squeeze in lemon juice and add freshly chopped parsley, adjusting salt and pepper to taste.

Serve the soup hot, garnished with extra parsley. Pair with crusty bread or a salad.