Preheat the oven to 375 degrees F and butter a 9-by-13-inch baking dish. Heat 1 tablespoon butter in a large sauté pan over medium heat. Add the garlic and cook until fragrant, 1 to 2 minutes. Add the bacon and cook until crispy and browned, another 5 minutes. Remove all but 1 tablespoon of the bacon fat. Add the chard and cook, stirring occasionally, until wilted, 4 to 5 minutes. Stir in the artichoke hearts, pickled jalapeños and sun-dried tomatoes; heat through, about 1 minute.
In a medium pot, melt the remaining 3 tablespoons butter over medium-high heat. Add the flour and cook, whisking, until golden, about 2 minutes. Reduce the heat to medium and slowly whisk in the milk. Cook, whisking constantly, until thickened, about 5 minutes. Add the sauce to the chard mixture. Stir in the ricotta, cream cheese, cheddar and parmesan. Season with salt and pepper.
Transfer to the baking dish. Sprinkle with more parmesan. Bake until golden brown and bubbling, about 20 minutes. Serve with pita chips or crackers.