The origins of this delicious sandwich go back to Italian immigrants in New Orleans. You can recreate an authentic version starting with fresh, homemade bread. Muffulettas make great hearty party food, plus you can prep everything the day before.
1 pound (500 g) assorted sliced deli meats (salami, ham and/or mortadella)
8 ounces sliced provolone OR mozzarella cheese
Olive Salad: Combine ingredients in medium bowl. Cover; refrigerate. Bread: Combine 2 cups flour, undissolved yeast, sugar and salt in large mixer bowl. Heat milk, water and oil to very warm (120° to 130°F); add to flour mixture. Beat 2 minutes at medium speed of electric mixer, scraping bowl occasionally. Stir in enough remaining flour to make a soft dough. Knead on lightly floured surface until smooth and elastic, about 8 to 10 minutes. Cover tightly with plastic wrap; refrigerate 8 to 24 hours. Divide dough in half; form each half into smooth ball. Place on large greased baking sheet; flatten each to 7-inch circle. Cover; let rise in warm, draft-free place until almost doubled in size, about 45 minutes. Brush tops with egg white; sprinkle with sesame seed. Bake at 400°F for 20 to 25 minutes or until done. Remove from sheet; cool on wire rack about 1 hour before making sandwiches. To assemble sandwiches: Split loaves in half horizontally. Top each bottom half with half of Olive Salad, spreading to within 1 inch of edge. Layer half of meat and cheese over Olive Salad; place tops on sandwiches. Cut each into 4 wedges.