Heat oil in a Dutch oven over medium-high heat. Add steak, onion, and garlic; cook 5 minutes or until steak is browned. Add beef broth and next 3 ingredients to pan; stir well to combine. Bring to a boil; reduce heat, and simmer, uncovered, 25 minutes, stirring occasionally.
Stir in carrot, mushrooms, and thyme; cover and simmer 30 minutes.
Combine flour and water in a small bowl, stirring with a whisk; add to steak mixture in pan. Cook over medium heat 2 minutes or until thick. Remove and discard thyme; stir in salt and pepper.
Preheat oven to 425°.
Spoon steak filling into a 9-inch deep-dish pie plate coated with cooking spray. Unroll pie dough; cut small slits in center to vent, and place over filling. Fold edges under; flute.
Bake at 425° for 17 to 18 minutes or until lightly browned.