Place the potatoes in a large pot, cover with cold water by 1 inch, and add a big pinch of salt. Bring to a gentle boil and cook until very tender, 12–15 minutes.
While the potatoes simmer, heat 1 tablespoon olive oil in a 10–12 inch oven-safe skillet over medium-high heat. Add onion and cook until translucent, about 3 minutes. Add ground beef and cook, breaking it up, until browned with little pink remaining, 5–7 minutes. Spoon off excess fat if needed.
Stir in garlic, thyme, rosemary, and smoked paprika; cook 30 seconds until fragrant. Push the beef to the sides of the skillet, add tomato paste and Dijon to the center, and cook 1 minute to caramelize. Toss to coat the meat.
Whisk the flour into the cold beef broth to make a smooth slurry. Pour it into the skillet along with Worcestershire, kosher salt, and black pepper. Reduce heat to medium and simmer, stirring, until the sauce is glossy and slightly thickened, 3–4 minutes. Fold in the peas and carrots and the parsley; cook 1 more minute. Remove from heat and taste for seasoning.
Drain the potatoes well, return them to the hot pot, and set over low heat for 30–60 seconds to steam off excess moisture. Mash with butter, warm milk, sea salt, and pepper until smooth but spreadable.
Heat oven to 375°F (190°C). Spoon the mashed potatoes over the beef mixture in the skillet, sealing to the edges to prevent bubbling over. Rough up the surface with a fork and brush lightly with 1 teaspoon olive oil.
Set the skillet on a rimmed baking sheet and bake until the filling is bubbling at the edges, 18–20 minutes. Switch the oven to broil and brown the peaks 2–4 minutes, watching closely.
Let the Shepherd’s Pie rest 10 minutes before serving so the layers set and slice cleanly.