Preheat the oven to 350 F
Heat a large Dutch oven over high heat with a 1 Tbsp of butter and 1 Tbsp olive oil. Dry pork with paper towels and season with salt and pepper. Sear each side of the pork for a few minutes until browned. Remove pork and set aside.
In the fat, toss in onions, garlic, thyme, and rosemary. Stir and lower heat to medium, cook for 5 minutes, until softened.
Nestle the seared pork in the middle of the pot. Pour in stock and rosé until the pork is almost completely submerged. Cover and place in the oven. Cook for 4 hours, flipping pork over a few times while cooking, until cooked thru and shreds easily.
Remove pork from pot and remove fat and shred meat.
Skim off any extra fat from sauce and return pork to sauce, stir together.
To grill the Radicchio slice through the root end so that the wedges stay together, drizzle with olive oil and grill on BBQ or a grill pan until charred and softened 10 min or so. Drizzle with Balsamic Vinegar.
To make Polenta, bring water, milk, and salt to a low boil, whisk in polenta, and whisk to combine, lower heat to simmer and cook for 30 minutes, stir frequently. Mix in the Pecorino and serve.
To serve, place a spoonful of polenta in middle of plate and top with pork and sauce, garnish with parsley, serve along with grilled radicchio.