Beat the softened cream cheese with the Italian dressing and oregano until smooth and pourable.

Spread the mixture over one tortilla, leaving a 1/2 inch border bare at the edges.

Layer half the salami, ham, and provolone evenly over the cream cheese, keeping it within an inch of center so it doesn't squeeze out.

Scatter half the banana peppers and dried lettuce over the meat and cheese.

Roll the tortilla tightly from the near edge, tucking the filling in as you go.

Wrap in plastic wrap and repeat with the second tortilla and remaining ingredients.

Chill the wrapped logs for at least 1 hour so the layers set and slice cleanly.

Unwrap, trim the ends, and cut each log into 8 rounds with a serrated knife.

Secure each round with a toothpick if it wants to unroll, then arrange cut-side up on a platter.