1. Place the potatoes in a large pot, cover with water, and bring to a boil. Reduce to a simmer and cook until potatoes are fork tender, 10-15 minutes.
2. Preheat oven to 375ᵒ F.
3. Grease a two-quart casserole dish and set aside.
4. Place a large skillet over medium heat, add the olive oil, swirl to coat the pan, and add the ground meat, breaking it apart as it cooks. When it is almost browned, add the diced onion (if using instead of onion granules) and stir to combine. Reduce the heat to medium-low and cook the beef and onion for 5 minutes, stirring frequently. Add the garlic granules, onion granules (if not using fresh onion), black pepper, 1 teaspoon salt, broth, and tomato paste, and stir until well combined. Add the frozen vegetables, stir to incorporate, reduce heat to low, cover, and let sit while you mash the potatoes.
5. Drain the potatoes, reserving some of the water (approximately ½ cup) discarding the rest. Return potatoes to the hot pot, add the butter or buttery spread, ¼ cup of the reserved cooking water, and ½ teaspoon salt. Mash potatoes and stir until ingredients are well mixed. Add extra water 1/8 cup at a time, if needed, until potatoes are creamy.
6. Transfer the cooked meat mixture into the prepared casserole dish and spread the mashed potatoes over the top; sprinkle with the grated cheese if using. Place a baking sheet on the middle oven rack and set the shepherd’s pie on top of the baking sheet (to catch the juices if they bubble over). Bake for 15 minutes, or until the cheese is melted and the shepherd’s pie is steaming hot; if more browning is desired, set the oven to broil for an additional 5 minutes, watching carefully to prevent burning.
7. Sprinkle optional garnish of parsley over the top and serve.