In a large pot, heat the butter over medium heat. Add the onion and garlic and cook until softened, about 5 minutes.
Add the cubed steak and kidney and cook until lightly browned, about 10 minutes.
Add the beef broth, tomato paste, Worcestershire sauce, and thyme and bring to a boil. Reduce heat to low and simmer, uncovered, for 30 minutes.
Mix the flour and milk together in a small bowl and add to the pot. Stir until the sauce has thickened, about 5 minutes.
Transfer the steak and kidney mixture to a 9-inch pie dish. Top with the puff pastry and cut a few small slits in the top. Bake for 30 minutes, until the pastry is golden brown.
Let cool for 10 minutes before serving.
Interesting Facts
Steak and kidney pie is a classic British comfort food dish.
The steak and kidney mixture can be made ahead of time and refrigerated until ready to use.
The pie can be served with mashed potatoes, green beans, or other vegetables.