For the polenta: Bring the chicken stock to a boil in a large pot. Add the polenta and whisk until fully incorporated, 3 to 4 minutes. Sprinkle with the salt and cook, covered, over medium heat for 5 to 6 minutes. Finish by folding in the melted butter. Keep warm while you prepare the chorizo.
For the chorizo: Coat a large saute pan with olive oil and set over medium-high heat. Add the onions and cook until almost translucent, and then add the ground pork. Brown 4 to 5 minutes while breaking the pork pieces up with the back of a wooden spoon. Add the paprika, granulated garlic, onion powder, chili powder and cumin, and sprinkle with salt and pepper. Cook 1 minute longer to toast the spices, and then add the vinegar, garlic and tomatoes. Simmer until the sauce is thickened and reduced, 8 to 10 minutes. Taste and season once more with salt and pepper. Keep warm.
For assembly: Wash, drain and finely slice the chard. Heat the garlic and some olive oil in a large pan and saute, 3 to 4 minutes. Season with salt and pepper. Drain in a colander and squeeze out any excess moisture.
Preheat the oven to 350 degrees F. Lightly grease an 8-by-8-by-2-inch gratin dish or an oval 9-inch cast-iron pan. Pour half of the polenta in and spread out evenly. Top with half of the chorizo and all of the Swiss chard. Sprinkle with half of each cheese. Repeat with a layer of the remaining polenta, then the remaining chorizo, and finally the remaining cheese. Cover with foil, place the dish on a sheet tray and bake 30 minutes. Remove the foil and bake until the cheese is golden and bubbly, 15 minutes longer. Let sit 25 minutes to set up, then cut into portions and serve.