Boil potatoes in cold water to cover with garlic and salt in a large heavy saucepan over high heat. Cook until easily pierced with a knife, 10–15 min. Drain potatoes and reserve the cooking water for mashing.

Heat cream, butter, and seasonings in a small saucepan over medium-low heat while potatoes cook. Place drained potatoes in a large bowl and add the warm cream mixture. Beat with an electric mixer until smooth, adding reserved potato cooking water as necessary until desired consistency is reached.

Fold parsley and lemon zest into mashed potatoes and serve.

Sear trimmed shanks in oil in a large stockpot or Dutch oven over high heat. Sear them two at a time, otherwise the pan will be too crowded to brown them properly. Once browned (about 5 min. per side), transfer shanks to a platter. Pour off any residual fat in the pan and return the pan to the burner.

Saute vegetables and herbs in 2 T. oil over medium-high heat, scraping up any brown bits in the pan. Cook until vegetables soften, about 8 minutes.

Add broth, wine, tomatoes, and paste; bring to a simmer. Return shanks to the pan (it’s okay if they stack on top of each other), cover, and bring liquid to a boil. Reduce heat to maintain a low, gentle simmer, adjusting the heat as needed. Cook shanks 1 hour, checking periodically to make sure the liquid is gently bubbling. After 1 hour, turn and rearrange the shanks, then cover and simmer another hour.

When shanks have braised for two hours, transfer them to a platter and skim off any visible fat floating on top of the braising liquid. Increase heat to high and bring liquid to a boil.

Combine vinegar and flour in a small dish, crushing lumps with your fingers. Whisk into boiling liquid to thicken slightly; boil for one minute to eliminate the starchy taste of the flour.

Finish the sauce with minced herbs and seasonings to taste. Add shanks back to the sauce and simmer 10–15 minutes to warm through.