Add 1/2 tbl of oil to a large skillet over medium heat. Brown half the pork shanks until golden brown, about 8 minutes per side. Set aside.
Repeat with the other 1/2 tbl of oil and the remaining pork shanks. Set aside with the other pork shanks.
Add the last 1/2 tbl oil to the skillet. Add the onion, carrot and garlic to the pan and soften, about 5 minutes.
Add the onion mixture to the bottom of a large slow cooker. Nestle the pork shanks on top.
Return the skillet to the stove over a low heat and use the juice of one lemon to deglaze the pan. Add the pan drippings to the slow cooker.
Add the mushrooms, oregano, thyme, basil, salt and lemon zest to the slow cooker.
Pour over both the chopped tomatoes and stock. Cook on high for 4 hours.
Remove pork shanks and set them aside, covered to keep them warm.
Remove all of the cooking liquid and half of the vegetables, adding them to a blender. Add the juice of the remaining lemon and puree until smooth. Check your seasoning here and add any extra salt if needed.
Return the vegetable puree to the slow cooker, stirring the remaining vegetables through the sauce. Add the pork shanks and cook for a further 30 minutes – 1 hour on low.