Step 1

Heat the oil in a large skillet over medium heat. Add the ham, onion, salt, and pepper; cook until the onion has softened some, 8 to 10 minutes. Add the garlic and thyme and cook until fragrant, about 1 minute; add the flour and cook for 1 minute more.

Step 2

Add the stock, increase the heat to bring to a boil, then reduce to a simmer, and cook until thickened, 3 to 5 minutes. Add the peas and carrots, remove from heat, taste, and season with more salt and pepper, if needed.

Step 3

Meanwhile, cover the potatoes in a pot with cold water by 2 inches. Bring to a boil, then reduce to a simmer, and cook until tender (a fork goes in with ease), 15 to 20 minutes; drain and transfer to a bowl.

Step 4

To the bowl, add milk and butter and mash until smooth and the butter has melted. Stir in the cheese, salt, and pepper until the cheese has melted; taste and season with more salt and pepper, if needed. Lastly, stir in the egg yolk.

Step 5

Heat the oven to 400˚F.

Step 6

You can either keep the ham filling in an oven-safe skillet or transfer to a baking dish. Spread the potato topping evenly over the top. (Optional: Create a design with a fork or other utensil.)

Step 7

Place the baking dish on a rimmed baking sheet to catch any potential spillover and bake until bubbling, 20 to 25 minutes. Broil until nicely browned on top, 1 to 2 minutes. Let cool slightly before serving.