In a large mixing bowl, combine the ground lamb, panko breadcrumbs, fresh mint, diced shallot, minced garlic, egg, kosher salt, and black pepper. Mix gently until just combined.
Form the mixture into golf ball-sized meatballs. You should yield about 12 to 16 meatballs.
Heat the olive oil in a large skillet over medium-high heat. Add the meatballs and pan-fry until browned on all sides, about 6 to 8 minutes. Remove the meatballs from the skillet and set aside.
In the same skillet, reduce the heat to medium and melt the butter. Pour in the dry red wine to deglaze the pan, scraping up any browned bits from the bottom. Simmer until the wine reduces by half.
Stir in the lamb or beef broth and the mint sauce. Bring the mixture to a gentle simmer.
Whisk the cornstarch with one tablespoon of cold water in a small bowl to create a slurry. Pour the slurry into the gently boiling gravy, stirring continuously until the sauce thickens and turns glossy.
Return the meatballs to the skillet, coating them evenly in the red wine gravy. Simmer for an additional 5 minutes until the meatballs are cooked through completely.
Serve the minted lamb meatballs hot, ladled generously over mashed potatoes and alongside boiled green peas.