Preheat oven to 350 degrees F. Also preheat large Dutch oven on medium-high heat and add 1 tablespoon of olive oil.
Season lamb shanks with 1/2 teaspoon salt and 1/2 teaspoon ground black pepper on all sides. Sear lamb shanks until golden brown crust forms and transfer to a large plate.
Add remaining 1 tablespoon olive oil and add onion, carrots and mushrooms. Saute until translucent, stirring occasionally. Then add rosemary, coriander and saute for another 30 seconds, stirring constantly. Add tomato paste and stir with vegetables until incorporated.
Pour in beef broth, red wine, balsamic vinegar, Worcestershire sauce and add remaining 1/2 teaspoon salt and 1/2 teaspoon black pepper, then stir. Add previously browned lamb shanks, making sure they are covered with liquids.
Cover pot with a lid and bake on a bottom oven rack for 2 hours.
After remove lambs shanks from the oven, let stand in a pot covered for about 10 minutes and serve hot with the gravy over mashed potatoes.
Notes
Store: Refrigerate for up to 5 days in an airtight container. Reheat desired amount in small pot by simmering on low heat. Cover and stir occasionally until warmed through.
Freeze: Make sure to cool lamb completely and then freeze in an airtight container for up to 3 months. Thaw in the fridge overnight.