Preheat the oven to 375 degrees F.

Place a stockpot over medium heat. Coat the bottom of the pan with olive oil and saute the shallot and garlic until lightly browned, 3 to 4 minutes. Add the Swiss chard and season with salt and pepper. Cook until the chard is wilted and tender, 3 to 4 minutes. Place the cooked chard in a strainer and cool in the refrigerator until chilled. Squeeze any excess moisture from the chard before continuing.

Lay out 1 sheet of phyllo dough lengthwise left to right and brush lightly with butter and season with salt and pepper. Place another sheet of phyllo on top and repeat this until there are 4 layers. Evenly cover the phyllo with slices of Swiss cheese, leaving 1 inch uncovered at the top and bottom of the sheet. Take half of the cooled chard and spread across the bottom of the phyllo sheet from side to side. Start at the bottom and carefully roll the phyllo up and around the chard like a sausage. Fold the ends of the log inward to seal. Brush the top with butter so it won't dry out and make another log with the remaining Swiss chard and phyllo dough. The logs can be made 1 day ahead and refrigerated. Place the logs on a sheet tray and bake for 15 to 20 minutes until golden and crispy. Let the rolls rest for 5 minutes and then slice using a serrated knife into 2-inch pieces. Serve hot or at room temperature.