Preheat oven to 325°F
Lay a sheet of phyllo dough on a clean dry work surface. Use a pastry brush to brush the phyllo sheet with melted butter. Fold the phyllo sheet in half lengthwise, resulting in a 12 by 8-inch rectangle. Brush the top of the phyllo with melted butter.
Place a few slices of smoked mozzarella at a narrow end of the phyllo rectangle, leaving 1-inch on each side. Top the cheese with a few pieces of sun-dried tomatoes.
Carefully roll up the phyllo dough into a cigar shape starting with the cheese and tomato end. About half way through the rolling, tuck in the 1-inch ends of the phyllo dough and continue rolling.
Place on a parchment-lined baking sheet, seam side down, and brush the top with butter. Continue rolling the 5 remaining cigars.
Bake until golden, about 25 to 30 minutes.