- Cook potatoes, covered with vented plastic wrap, in a microwave-safe bowl for 5 minutes, stirring once.
- Meanwhile, season steaks with salt and pepper. Heat a 12-inch skillet over medium-high heat; add 1 teaspoon of the oil. Add steaks; cook 3 to 4 minutes per side. Transfer to a platter; cover to keep warm. For sauce, in the same skillet cook tomatoes and garlic in 1 teaspoon of the oil until softened. Stir in olives and oregano; cook for 3 minutes more.
- In a separate nonstick skillet cook potatoes in 2 teaspoons hot oil over medium-high heat for 4 minutes. Season to taste with salt and pepper. Serve steaks and potatoes with sauce.
- Preheat oven to 350 degrees.
- Pat beef dry with paper towels and season with salt and pepper. Heat 1½ tablespoons oil in Dutch oven over medium-high heat until just smoking. Add half of beef and cook until well browned all over, 7 to 10 minutes. Using slotted spoon, transfer beef to bowl with remaining uncooked beef.
- Add remaining 1½ tablespoons oil to now-empty pot and reduce heat to medium. Add onion, and carrots and cook until vegetables are lightly browned, about 5 minutes, scraping up any browned bits. Stir in tomato paste and garlic and cook until fragrant, about 30 seconds.
- Stir in flour until vegetables are well coated and cook for 1 minute. Stir in broth, soy sauce, Worcestershire, and bay leaf until combined. Add beef and bring to simmer. Cover and transfer to oven. Cook until beef is tender, about 1 hour.
- Remove filling from oven and increase oven temperature to 400 degrees. Transfer filling to 9-inch deep-dish pie plate; discard bay leaf. Let filling cool, uncovered, for 30 minutes. Stir in 1 teaspoon chopped thyme. Season with salt and pepper to taste.
- Top filling with pie dough so dough overhangs edges of pie plate slightly. Fold overhanging pie dough inward so folded edge is flush with inner edge of pie plate. Crimp dough evenly around edge of pie using your fingers.
- Cut a decorate shape out of left over pie crust andn place in middle of pie. Cut six ½-inch slits around center, halfway between center and edge of pie. Brush dough with remaining egg, then season with salt, pepper, and remaining ½ teaspoon chopped thyme. Transfer pie to rimmed baking sheet and bake until crust is golden brown, about 30 minutes. Transfer pie to cooling rack and let cool for 20 minutes. Serve.