Preheat oven to 325°F (160°C)
Pat lamb shanks dry and season generously with salt and pepper
Heat olive oil in a large Dutch oven over medium-high heat and sear shanks on all sides until deeply browned (~4-5 mins per side), then remove and set aside
In the same pot, sauté onion and carrots until softened (~5 mins)
Add garlic and tomato paste, cooking for 1 minute until fragrant
Pour in red wine, scraping up browned bits, and simmer until reduced by half (~5 mins)
Add stock, rosemary, thyme, and bay leaves, then return lamb shanks to the pot ensuring they're mostly submerged
Cover and transfer to the oven, braising for 2.5–3 hours, turning shanks halfway, until meat is fork-tender
Place pumpkin cubes in a pot of salted boiling water or steamer basket and cook until fork-tender (~12–15 mins), then drain well
Mash the cooked pumpkin with butter, heavy cream, maple syrup, cinnamon, nutmeg, and ginger, then season with salt and white pepper
Toss cherry tomatoes, zucchini, and carrots with olive oil, oregano, salt and pepper, then roast until tender
Strain the braising liquid and reduce it further if desired, optionally finishing with butter for gloss
