Preheat oven to 350°F
Pat short ribs dry, season generously with salt and pepper, then dredge lightly in flour
Heat oil in a large Dutch oven over medium-high heat and sear ribs on all sides until deeply browned (about 2-3 min per side)
Remove ribs and set aside
Lower heat to medium and add onion, celery, and carrots to the pot and sauté until softened and lightly golden
Add halved garlic bulbs and rosemary sprigs, stirring briefly until fragrant
Pour in red wine and beef broth, scraping up all the browned bits
Stir in brown sugar and peppercorns and bring to a gentle simmer
Return short ribs to the pot, nestling them into the liquid
Cover and braise in the oven for about 3 hours, or until meat is fall-off-the-bone tender
Remove ribs and keep warm
Strain the cooking liquid into a saucepan and simmer 15-20 minutes until reduced
Whisk in butter to finish the gravy
Boil potatoes until fork tender
Drain and mash in a large bowl
Blend in milk until smooth
Melt butter with garlic and mix in
Salt to taste
Fold in mozzarella while hot
