Preheat oven to 250°F. Heat a large Dutch oven over medium-high heat.
Season shanks all over with salt and pepper. Add lard to Dutch oven and swirl to coat the pan. Add in shanks, working in batches. Cook for 2-3 minutes per side or until browned.
Move shanks to a plate and set aside. Reduce heat to medium-low.
Add butter to Dutch oven and swirl to coat the pan. Add in carrots, celery, onion, and garlic. Cook for 5-8 minutes, stirring frequently, until vegetables are fragrant but not browned and have absorbed most of the liquid in the pan.
Add in tomato paste and stir to coat vegetables. Cook for 1 minute.
Add in flour and stir to coat vegetables. Cook for an additional 1-2 minutes.
Add in wine and stir to combine. Cook for 2-3 minutes or until thick and bubbly. Add in stock or broth, salt, and pepper and stir to combine. Add in rosemary, thyme and bay leaves.
Add shanks back to pan. Make sure they are completely submerged in the liquid.
Place lid on Dutch oven and bake for 7-8 hours or until tender.
Remove shanks to a plate. Remove thyme, rosemary, and bay leaves and discard.
Bring sauce to a boil over medium heat. Simmer until thickened and reduced slightly, about 20 minutes.
You can remove the meat and connective tissue from the bones before serving or serve the meat with the bone still attached.
Serve over mashed potatoes (see below) and pour sauce with vegetables over the top. Don't forget to scoop the marrow out of the bones for an extra treat!
Bring a large pot of water to a boil. Add in potatoes and cook until tender, about 20-25 minutes.
While potatoes are cooking, melt butter in a medium saucepan over medium-low heat. Continue cooking butter until browned, stirring frequently, about 20 minutes.
Once potatoes are tender, place them in potato ricer, working in batches. Rice the potatoes into a large mixing bowl. You can rice them twice for extra creamy potatoes.
Once butter is browned, strain it with a fine mesh strainer into the mixing bowl. Add in half and half (a little at a time, you might not need all of it) and salt and pepper. Using a hand mixer or stand mixer, mix on medium-low speed until fluffy, about 5 minutes.