Preheat oven to 400°F with a rack set in center. Oil a metal 2-qt. baking pan that’s about 7x11 inches and 2 inches deep, or use a 9-inch square pan. (You’ll be browning the shepherd’s pie under the broiler before serving, so don’t use a glass baking dish, which could break.)

Heat 1 Tbsp. oil in a large frying pan over medium-high heat. Add onion and garlic and cook, stirring occasionally, until onion is tender, about 5 minutes. Stir in ground lamb and cook, stirring often, until meat is browned and crumbly, about 8 minutes.

Meanwhile, in a small bowl, whisk together broth, Worcestershire sauce, soy sauce, tomato paste, and flour. Also heat potatoes according to package directions.

Drain fat from meat if needed. Stir in frozen vegetables. Add broth mixture to pan and bring to a simmer over medium-high heat. Cook, stirring often, until gravy is thickened, about 5 minutes.

Transfer meat mixture to the prepared baking pan. Dollop hot mashed potatoes over the top and spread in an even layer.

Bake shepherd’s pie until edges are bubbly, 20-25 minutes.

Increase oven temperature to broil, still leaving pan in the center of the oven. Broil to brown the mashed potatoes, 2-3 minutes. Sprinkle shepherd’s pie with parsley before serving.