Bring a large pot of salted water to a boil over medium heat. Add the potatoes and cook until just tender. Drain and turn out onto a cutting board. Smash the potatoes with the side of a large knife or spatula.
Heat a large cast iron skillet over medium-high heat and add the olive oil. When the pan is very hot, but not smoking, add the cipollini onions, and cook until starting to caramelize, about 4 to 5 minutes Add in the drained artichokes and season with salt and pepper, to taste. Cook for 2 to 3 minutes before turning them so that they will caramelize. Add the potatoes and cook until the potatoes are starting to brown, then stir in the garlic and the thyme. Slowly pour in the chicken stock, scraping up the bits from the bottom of the pan. Sprinkle with the vinegar and adjust seasoning with salt and pepper, if necessary. Transfer to a platter and garnish with chopped parsley.