Quarter the leeks lengthwise and slice ¼″ thick. Soak in cold water in a roomy mixing bowl for a few minutes, letting any dirt fall to the bottom, then scoop out with a slotted spoon and dry on a towel. Cut the artichoke hearts into eighths around the center axis.
Preheat oven to 400 (F). Melt butter over medium heat in a large skillet, then add leeks, garlic, and rosemary. Cook for a few minutes, until leeks have softened.
Add artichokes, ½ teaspoon salt, and 1 cup of the liquid. Adjust heat to a simmer, stirring occasionally, until liquid has nearly evaporated, about 10 minutes.
Turn off heat and add beans and seasoning to taste, depending on how much salt was in the canned beans.
Spread bean and vegetable mixture in a 1.5 to 2 qt. ungreased baking dish, add remaining ¾ cup liquid to almost cover, then top with all the goat cheese.
Mix bread crumbs and olive oil and layer evenly over the goat cheese. Bake about 25 minutes, until topping has browned.
Let cool a few minutes before serving.
