Preheat oven to 375°F (190°C).
In a bowl, mix flour and salt. Cut in butter until mixture resembles coarse crumbs. Stir in water until dough forms. Divide in half, wrap in plastic, and refrigerate.
In a skillet, cook beef, onion, and garlic over medium heat until meat is no longer pink. Drain fat.
Stir in broth, Worcestershire sauce, thyme, rosemary, salt, and pepper. Simmer for 5 minutes.
Roll out half of the dough and fit into a 9-inch pie plate. Fill with meat mixture.
Roll out remaining dough and place over filling. Seal and flute edges. Cut slits in top. Brush with beaten egg.
Bake for 45-50 minutes or until golden brown. Let stand 10 minutes before serving.