In a big saucepan, warm the olive oil over medium heat. Stirring constantly, sauté the onions and celery for three minutes.
Add the pepper, garlic, and Italian seasoning. Cook, stirring constantly, for one minute.
Add the butter after that. Mix until the substance dissolves. After that, whisk in the flour and cook for one to two minutes.
Stirring constantly, slowly scrape the crumbs from the pot's bottom before adding the broth.
Increase the heat and boil, which should take two minutes. To the saucepan, add the potatoes and artichokes. Once the broth reaches a rolling boil again, reduce the heat to medium-low, cover, and simmer the soup until the potatoes are very tender—about 30 to 35 minutes. If you pierce them with a fork or knife, they should come apart effortlessly.
Once the saucepan is no longer simmering, turn off the heat and cover it. Using a handheld immersion blender, process the soup in the pot until it reaches the desired texture or is smooth. Use a regular blender instead of an immersion blender if you don't have one (see notes).
If necessary, taste and add salt. For comparison, we added a tsp to ours.
If preferred, top the creamy artichoke soup with grated parmesan cheese and chopped parsley.