Boil the potatoes for the topping: Peel the potatoes and minimize 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 keep up 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 often, 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 effectively. Scatter the butter items excessive. Add the Parmesan, salt, and pepper.
With a picket spoon or rubber spatula, stir a couple of occasions, till the butter is usually 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 needs 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 heart 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 prepare dinner till it’s starting to brown, about 3 minutes.
Add the garlic and tomato paste. Stirring repeatedly, prepare 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, fastidiously drain it off (this shouldn’t be an issue in case your beef is round 93% lean).
Sprinkle the flour excessive, and prepare dinner, stirring repeatedly, 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 regulate the seasoning as desired.
Stir within the peas and carrots.
Switch the meat combination to the ready dish, spreading it into an excellent layer.
Add the mashed potatoes by spoonfuls excessive, beginning across the edges to create a “seal” (this can stop the filling from effervescent up). With a spatula, gently unfold the potatoes into an excellent layer.
Line a rimmed baking sheet with a chunk of parchment paper, then place the dish on high (this can catch any components 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 very least 10 minutes previous to serving.