
This comfort food mash-up combines a ground beef and vegetable mixture with fluffy mashed potatoes, all wrapped in a golden brown pie crust.
Arrange a rack in center of oven; preheat to 425°. Place potatoes in a medium saucepan and cover with cold water by 1"; season with 1/2 tsp. kosher salt. Bring to a boil over high heat and cook, stirring occasionally, until potatoes are tender enough to mash with little to no resistance, about 10 minutes.
Meanwhile, in a large stainless steel skillet over medium-high heat, heat oil; swirl to coat skillet. Add ground beef; season with 1 tsp. kosher salt and 1/2 tsp. pepper. Cook, breaking up beef into small pieces with a spoon, until browned and cooked through, 5 to 7 minutes. Transfer beef to a plate. Pour off all but 2 Tbsp. fat.
In same skillet over medium heat, combine onion and carrot; season with 1/4 tsp. kosher salt. Cook, stirring occasionally, until onions begin to soften and are slightly translucent, about 5 minutes. Add garlic, rosemary, and thyme and cook, stirring, until fragrant, about 1 minute more.
Return beef to skillet along with any accumulated juices. Stir in tomato paste. Add wine, scraping up bits from bottom of pan, and cook, stirring, until wine is mostly evaporated, about 1 minute. Stir in broth and Worcestershire, then sprinkle in flour. Cook, stirring, until sauce is slightly thickened, 2 to 3 minutes. Stir in corn and peas; season with 1/2 tsp. kosher salt.
Drain potatoes, then quickly return empty saucepan to stove. Heat over medium-low heat and add half-and-half, butter, and remaining 3/4 tsp. kosher salt and 1/2 tsp. pepper. Cook, stirring, until butter is melted, about 2 minutes. Add potatoes and mash with a fork or potato masher until smooth. Stir in Parmesan.
On a lightly floured surface, roll 1 batch of dough to a 11" round. Unfurl into the bottom of a 9" pie dish. Add beef mixture; smooth in an even layer. Top with mashed potatoes; smooth in an even layer and spread to the edges.
On lightly floured surface, roll remaining pie dough to a 9" round. Arrange on top of mashed potatoes. Press edges of top and bottom dough rounds together. Using a sharp knife or kitchen shears, trim edges of dough, leaving about a 1/4" overhang. Fold excess underneath dough on top rim of pie dish. Using clean fingers, crimp to seal.
Brush top of pie all over with beaten egg. Cut 4 slits into the top to vent. Sprinkle with sea salt.
Bake shepherd’s pot pie, covering edges with foil if browning too quickly, until top is golden brown, about 45 minutes. Let cool 15 minutes before slicing.