In a medium soup pot, over medium heat, sweat the onions and garlic with the butter. Stir until translucent. About 3 to 5 minutes.
Add the tomatoes, bell pepper, bacon bits, and rosemary along with a bit of salt and pepper. Bring the mixture to a simmer. Allow it to simmer for about 20 minutes, stirring occasionally.
If making true stew: If you want this to be a true stew, you can add the chicken, mushrooms, and capers, at this point. I’d wait until the chicken is cooked through, before adding the artichokes, and they’ll likely just fall apart, if you add them too early.
However, I decided to split this dish into two parts. So, while the tomatoes simmer, gather your chicken, mushrooms, artichoke hearts, coarsely chopped capers, and chopped rosemary.
Pre-heat a very large sauté pan (or two medium to large ones) over high heat. Pour half the olive oil into the pan(s) and spread it around. Evenly sprinkle the chicken cubes around the base of the pan, keeping a bit of space between each nibblet. If too much is added, the pan will cool too much and the chicken will just simmer and steam. Once the chicken is in the hot pan(s), season with a bit of salt and pepper.
Once the chicken has a bit of color, toss the chicken in the hot pan, to brown another side of the cubes. Add the mushrooms to the pan, along with a bit of salt and pepper. Cook this mixture over high heat, stirring or tossing the pan every minute or so.
Once the chicken and mushrooms are almost completely cooked through, add the cream to the tomato soup base and bring it up to a slow simmer.
Add the artichokes, capers, and rosemary to the hot chicken pan and toss the ingredients together. Allow this mixture to cook for another minute, or until the chicken is completely cooked through. Turn the hot pan off and leave it sitting on the stove.
Puree the hot soup base in a blender, until smooth.
Divide the chicken mixture between 8 different soup bowls. Pour the creamy tomato soup base around the chicken. Finally, drizzle a bit of the remaining olive oil over the tops of each bowl. Serve!
If making true stew: If you’ve skipped most of the above steps and are simply making a big creamy stew (which will be phenomenally delicious!), once the chicken is soft and shreddable (about 20 to 25 minutes), add the artichokes and cream, then bring up to a very low simmer. Taste, then adjust the seasoning. Divide between 8 bowls, drizzle some olive oil over the top. Serve!