Heat oven to 400° F. Unroll crust and roll out slightly. Fit into the bottom and up the sides of a 9-inch deep pie dish. Flute edge. Line crust with nonstick foil. Bake at 400° F for 12 minutes. Remove foil.
Meanwhile, cook beef in a large nonstick skillet over medium-high heat, 5 minutes, breaking apart with a spoon. Spoon into a bowl and stir in ketchup and Worcestershire sauce.
In same skillet, cook onion for 5 minutes over medium heat. Add spinach and tomatoes; cook 3 minutes. Season with 1/8 teaspoon each of the salt and pepper. Stir in beef.
Transfer beef mixture to crust. In medium bowl, whisk together eggs, milk, mustard and remaining 1/8 teaspoon each salt and pepper. Sprinkle cheese over filling. Carefully add egg mixture. Bake at 400° F for 35 to 40 minutes. Let stand 5 minutes before slicing.