Step 1

Heat oven to 375°F. Heat the oil in a 9-inch cast-iron skillet over medium heat. Add the beef, mushrooms and 3/4 teaspoon each salt and pepper, and cook, breaking up the beef with a spoon, until browned, 4 to 6 minutes. Spoon off and discard any fat.

Step 2

Add the tomato paste and cook, stirring, for 2 minutes. Stir in the onions and thyme, then sprinkle with the flour and cook, stirring, for 30 seconds.

Step 3

Add the stout and simmer until the liquid has thickened, about 1 minute. Add 1/2 cup water and bring to a simmer. Add the squash and peas, return to a simmer, then remove from heat. (This whole step takes only 2 to 3 minutes total.)

Step 4

Unroll the pastry on a cutting board, brush with the egg, then cut a cross in the center. Lay the dough on top of the beef mixture (egg-side up), gently pressing the edges around the inside of the skillet. Bake until golden brown, 30 to 35 minutes. Let rest for 5 minutes before serving.