Start the polenta at least 8 hours ahead. Whisk together the polenta and boiling water in a large pot. Cover, and let sit at room temperature for at least 8 hours, and up to 12.
Heat a gas or charcoal grill to medium heat.
Combine the tomatoes, 1 ½ Tbsp olive oil, 1 Tbsp basil, garlic, balsamic vinegar, salt and pepper in a medium bowl. Line a grill basket with aluminum foil and pour tomato mixture into it. If you don’t have a grill basket, just wrap the tomato mixture in a foil packet - I recommend multiple layers of foil to prevent leaking.
Peel onion, and slice crosswise into medium-thick slices. Brush tops and bottoms of slices with the remaining ½ Tbsp olive oil and sprinkle with salt and pepper.
Grill onion slices, italian sausages, and tomato mixture until onions are caramelized, sausages are browned and cooked through, and tomatoes have burst and simmering in their juices, about 10-15 minutes.
While everything is grilling, start the polenta. Whisk 1 ½ cups water and salt into the polenta mixture in the pot and bring to a boil over medium high heat. When mixture thickens, reduce heat to low and simmer, stirring occasionally until polenta becomes creamy and thick. Stir in the butter and cheeses and season to taste with additional salt if needed. Pour finished polenta into a large dish just before serving.
Chop sausages and onions into bite-sized pieces. Combine in a bowl with the tomato mixture, then pour atop polenta. Garnish with fresh basil leaves and serve with plenty of grated parmesan to pass.