Preheat the oven to 400 degrees F. Cut the bread in half, then cut each half crosswise into 4 strips; toss with 1 tablespoon olive oil and the sage and season with salt and pepper. Put 1 strip of bread and 1 provolone stick across the center of each chicken cutlet. Tightly roll up the chicken around the bread and cheese, then wrap each roll with a piece of pancetta and secure with a toothpick.
Heat a large ovenproof nonstick skillet over medium-high heat; add 2 tablespoons olive oil. Add the chicken; cook, turning, until browned, 4 minutes. Add 3/4 cup chicken broth. Transfer the skillet to the oven; cook until the chicken is golden and cooked through, 7 to 8 minutes.
Meanwhile, heat the remaining 2 tablespoons olive oil in a large skillet over medium-high heat. Add the garlic and cook until slightly golden, about 30 seconds. Add the beans and cook, stirring, until warmed through, about 2 minutes. Add the escarole, the remaining 1/4 cup chicken broth, 1/2 teaspoon salt and a few grinds of pepper. Cook, stirring occasionally, until the escarole is tender, 7 minutes.
Remove the chicken from the skillet using a slotted spoon. Cook the pan juices in the skillet over medium-high heat until reduced by half, about 5 minutes. Remove from the heat and swirl in the butter. Serve the chicken with the pan sauce and escarole mixture.