Cut the meats and the sausages in medium-sized pieces. Heat the lard and the oil in a pan and slowly fry the meats until they starts changing their color into an even whitish.
Cover the pan and let the meats simmer for 5 more minutes, then take the lid off and let the meat juice boil away. Once the juice has evaporated and the meat starts getting fried once again in the hot oil, add the sausages, and season with salt and pepper.
While the ‘tochitura’ is frying, start working on the polenta, so that you complete both of them roughly at the same time.
Bring the water – with a pinch of salt – to a boil, over medium-high heat. When the water is nearly boiling, add just a bit of corn flour. Once the water starts boiling, add the rest of the corn flour, and keep stirring the mixture with a whisk, to avoid getting any lumps.
Make one sunny-side up egg for each plate, and grate the cheese.
Put some polenta on each plate. Add grated cheese on top of it, then the sunny-side up egg as a topping. Season with salt and pepper, then nicely arrange the pieces of meat and sausages around the polenta.