Preheat the oven to 375°F.
Score the skin of the pork belly lightly and season with salt and pepper.
In a heavy skillet, sear the pork belly over medium-high heat until the skin is crispy, about 2-3 minutes per side.
Transfer the pork belly to a slow cooker or an oven-safe pot, add 2 crushed garlic cloves, a few sprigs of rosemary and thyme (reserve 1 tbsp each chopped for the vegetables), and a splash of water or low-sodium broth if desired for moisture.
Slow-braise the pork belly in the oven at 375°F for 1.5 to 2 hours until tender and much of the fat has rendered out.
Meanwhile, peel and dice the carrot, parsnip, and turnip into evenly sized cubes. Toss them with the reserved rosemary, thyme, olive oil, salt, and pepper.
Spread the vegetables on a baking sheet and roast in the oven alongside the pork belly (or after removing the pork) for 25-30 minutes, until tender and lightly caramelized.
Poach the eggs in simmering water with a splash of vinegar for about 3-4 minutes for soft-set yolks.
Slice the pork belly into bite-sized pieces, plate with a generous serving of the herb-roasted root vegetables, and top with the poached eggs.
Serve immediately and enjoy this balanced dish of rich, tender pork with vibrant, earthy vegetables and a protein-packed poached egg topping.