1. Bring a large pot of lightly salted water to a boil over high heat. Add the artichokes and place a heatproof bowl or plate on top to keep them submerged. Cook until the artichokes are very tender and the leaves are easy to pull off, 45 minutes to 1 hour. Drain and rinse under cold water until cool enough to handle.

2. Working with one artichoke at a time, pull off the leaves until you reach the thin core of very tender leaves. Place the leaves in a plastic bag and refrigerate to serve with the dip, if desired. Pull off the core to reveal the heart. Using a dessert spoon, scoop out and discard the fuzzy choke. Using a small sharp knife, trim off any tough skin from the hearts and the stems, if attached (the inner stem has the same flavor as the heart). Chop the heart and stems into ½-inch cubes.

3. Mix the chopped artichoke, havarti, Parmesan, mayonnaise, dill, and garlic in a medium bowl. Transfer to a 3- to 4-cup baking dish. (The dip can be covered and refrigerated for up to 1 day.)

4. Position a rack in the center of the oven and preheat the oven to 350°F.

5. Sprinkle the bread crumbs on the dip and drizzle with the oil. Bake until the dip is bubbling, 20 to 30 minutes (longer if it’s been refrigerated). Serve hot.

Original Artichoke Dip: Mix ½ cup Hellmann’s or Best Foods mayonnaise, ½ cup sour cream, one 14-ounce can artichoke hearts, drained and chopped, 1/3 cup freshly grated Parmesan, and 1/8 teaspoon hot red pepper sauce. Bake as directed.