In a large, heavy pot, heat the olive oil over medium heat. Once hot, add the onions, celery, and carrots. Stir occasionally, allowing the vegetables to soften for 5 to 7 minutes.

Mix in the minced garlic, rosemary, red pepper flakes, salt, and pepper. Stir well, cooking for an additional 30 seconds to let the garlic release its flavor.

Sprinkle the flour over the sautéed vegetables and stir continuously for about 1 minute, until the mixture becomes a light golden color and smells nutty.

Gradually pour in 2 cups of the broth, whisking to avoid any lumps. Continue to whisk until the mixture thickens.

Add the remaining broth and bring the soup to a boil. Lower the heat to a gentle simmer.

Stir in the diced potatoes and add the bay leaf. Cook with the lid slightly ajar, allowing the potatoes to become tender, which takes about 20 minutes.

Lower the heat, remove the bay leaf, and gently stir in the half and half (or cream) along with the shredded cheese if using.

Check the seasoning and adjust with additional salt and pepper as needed.

To serve, top the soup with your preferred garnishes. If a creamier texture is desired, mash some of the potatoes with a potato masher or blend a portion of the soup using an immersion blender, then mix it back into the pot. Enjoy!