Preheat oven to 450°. In a 2-qt. glass measuring cup or microwave-safe bowl, combine polenta, 5 cups water, and 1/2 tsp. salt. Microwave, stirring every 5 minutes or so, until polenta is thick and tender, 25 to 30 minutes total.
Meanwhile, on a rimmed baking sheet, toss sausages, broccoli romanesco, onion, mushrooms, 2 tbsp. oil, and 1/2 tsp. salt. Roast until browned, stirring occasionally, 25 to 30 minutes total.
In a food processor, pulse remaining 2 tbsp. olive oil, the parsley, thyme, pine nuts, capers, lemon zest, and lemon juice until parsley is minced. Add to sausage mixture and toss to combine. Season to taste with more salt.
Stir butter and grated parmesan into polenta. Spoon polenta onto a rimmed platter and top with sausage mixture. Serve with shaved parmesan to sprinkle on top.