In a large nonstick saute pan over medium-high heat, cook bacon until crispy and fat has rendered, 8 to 10 minutes. Add half the chard and stock. Season with salt and pepper. Cook until wilted, 2 to 3 minutes. Transfer to a plate and set aside. Repeat with remaining bacon fat and chard.
Remove from heat, sprinkle with Parmesan, and toss before serving.