Cut each cheese slice in half; place 1 half on top of each cutlet. Starting with a short end, tightly roll up cutlets, jelly-roll style. Tie securely with string.
On waxed paper, combine flour and pepper. Mix well. Add cutlets; toss gently to coat.
In a large nonstick skillet, melt butter over medium heat. Add cutlets; cook turning frequently, until golden, about 3 minutes.
Add broth, wine, and dried oregano to skillet. Increase heat; bring to a boil. Reduce heat to medium-low; simmer until chicken is cooked through and sauce is slightly thickened, about 10 to 12 minutes. Place on a serving plate; remove string.