Heat the olive oil in a large Dutch oven or heavy bottomed soup pot over medium heat. Drain the artichoke pieces and pat very dry. Place the artichokes, potatoes, and shallots then cook, stirring occasionally, until the vegetables are lightly browned and barely tender, about 20 minutes. Add the minced garlic and cook for 1 minute, stirring constantly. Add the wine and cook until nearly evaporated, about 7 minutes. Add the chicken broth, Parmesan rind, and thyme sprig and bring to a boil. Reduce the heat to medium low, cover partially, and cook about 45 minutes, or until the veggies are very tender. Discard the thyme bundle and Parmesan rind.