Boil the potatoes for the topping: Peel the potatoes and lower into 1-inch chunks. Place in a medium saucepan. Add sufficient cool water to cowl the potatoes by 1 inch. Cowl the pot and produce to boil over excessive warmth. As quickly because the water is boiling, uncover, then scale back the warmth to a simmer. Cook dinner, adjusting the warmth as wanted to take care of a mild, regular simmer, till potatoes are fork tender, about 12 to 16 minutes. Drain the potatoes and return them to the saucepan. If the potatoes are very moist, warmth the saucepan over low, shaking it sometimes, till any liquid on the floor of the potatoes has cooked off, about 1 minute, then take away from the warmth.
Combine the topping collectively: With a potato masher or picket spoon, mash the potatoes nicely. Scatter the butter items excessive. Add the Parmesan, salt, and pepper.
With a picket spoon or rubber spatula, stir a number of occasions, till the butter is generally melted.
In a small bowl or liquid measuring cup with a spout, whisk collectively the milk and egg yolk.
Add to the potatoes. Stir to mix. The potatoes ought to be wealthy and fluffy.
Make the filling: Coat a 9×9, 8×10, or 11×7 casserole dish with nonstick spray. Place rack within the middle of your oven and preheat to 400℉. In a big skillet, warmth the oil over medium-high warmth. As soon as it’s sizzling and shimmering, add the onion and cook dinner till it’s starting to brown, about 3 minutes.
Add the garlic and tomato paste. Stirring constantly, cook dinner 30 seconds.
Add the meat (or lamb), salt, and pepper. Cook dinner, breaking up the meat, till it’s browned and cooked by way of, about 4 minutes. If there may be extra grease within the pan, rigorously drain it off (this shouldn’t be an issue in case your beef is round 93% lean).
Sprinkle the flour excessive, and cook dinner, stirring constantly, for 1 minute.
Stir within the broth, Worcestershire, thyme, and bay leaf. With a rubber spatula or picket spoon, scrape the underside of the pan to take away any stuck-on browned bits. Deliver the liquid to a boil, scale back the warmth to low, then cowl the pan and let simmer gently till the sauce thickens barely, about 10 minutes. Take away the thyme and bay leaf. Style and modify the seasoning as desired.
Stir within the peas and carrots.
Switch the meat combination to the ready dish, spreading it into a good layer.
Add the mashed potatoes by spoonfuls excessive, beginning across the edges to create a “seal” (it will stop the filling from effervescent up). With a spatula, gently unfold the potatoes into a good layer.
Line a rimmed baking sheet with a bit of parchment paper, then place the dish on prime (it will catch any elements of the filling that bubble over). Bake the shepherd’s pie uncovered on the middle rack for 25 minutes, or till the potatoes start to brown. Let cool for at the least 10 minutes previous to serving.
