Peel potatoes and cut into roughly 1-inch pieces. Place in a large saucepan, cover with salted water and bring to a boil. Cook until potatoes are tender but not mushy.
While potatoes are cooking, prepare the dressing. In a large bowl, whisk together oil, mustard, lemon zest, lemon juice, minced garlic, salt and pepper.
Once potatoes are tender, drain thoroughly and toss, while still hot, with the dressing. Add chopped artichoke hearts and dried tomatoes and combine. Allow to cool to room temperature and check for seasoning. Add more salt and/or pepper to taste, and serve.