Heat up oil in a Dutch oven pot on medium heat, cook the lamb shanks until the outside is golden brown all over. Then remove onto a plate and set aside.
Melt 2 tbsp butter into the pot and cook the chopped onions and diced carrots until soft.
Add in minced garlic and cook until fragrant (about 1 minute).
Then add in tomato sauce and stir until vegetables are coated.
Pour in beef broth and tomato paste, mix until well-combined then return the lamb shanks into the pot.
Add in rosemary and bring to a boil.
Cover the pot and transfer it into the preheated oven. Cook for 2 hours until the lamb shanks are tender.
Once done, remove the lamb shanks from the pot and place them in foil to keep warm.
Place the pot back onto the hob. Add in wine and bring to a boil over medium heat.
Then reduce the heat and let it simmer for about 10 minutes until the sauce thickens. Stir in 2 tbsp butter.
Sauce and lamb shanks are ready.
Mashed Potatoes
Cut the potatoes into even pieces and cover with water in a pot. Add in a pinch of salt.
Bring to a boil and cook until potatoes are just soft.
Drain the cooked potatoes and put them back into the pot.
Mash them until smooth (or to your preference if you prefer some bite-size chunks).
In another pot, melt butter in milk over low heat.
Once fully melted, pour the mixture into the mashed potatoes.
Stir until well-combined and creamy.
Then add in sour cream and continue mixing until well-combined.