Put the oil in a large skillet over medium-high heat. When it's hot, add the sausages and cook, turning occasionally, until they're nicely browned on all sides and cooked through, about 20 minutes. Set aside.
In a medium saucepan, add the cornmeal along with 1 cup water and whisk well to make a slurry; continue whisking to eliminate any lumps. Place the pan over medium-high heat, sprinkle with salt, and bring to a boil. Reduce the heat to medium and continue to cook, whisking frequently and adding water as needed to keep the polenta smooth and free of lumps (this will take between 3 and 4 more cups of water depending on the grind of your polenta). Cook until the polenta is tender and creamy, 15 to 30 minutes. If the mixture becomes too thick, add a bit more water to thin it; you're looking for a consistency similar to sour cream.
Add the butter and taste; season with salt if necessary, and sprinkle with lots of pepper. Spoon the polenta into serving bowls and top with sliced sausage. Makes 4 servings.