- Combine potatoes and 1 tablespoon salt in medium saucepan and cover with water by 1 inch. Bring to boil over medium-high heat and cook until tender, 10 to 12 minutes. Drain potatoes and return them to saucepan. Add half-and-half, 4 tablespoons butter, and 1/4 teaspoon pepper and, using potato masher, mash until smooth. Cover and set aside.
- Melt remaining 1 tablespoon butter in 10-inch skillet over medium heat. Add carrots and onion and cook until softened, about 4 minutes. Add beef, 1/2 teaspoon salt, and 1/4 teaspoon pepper and cook, breaking up meat with spoon, until beef is no longer pink, 4 to 6 minutes.
- Stir in tomato paste, garlic, and thyme and cook until fragrant, about 1 minute. Stir in flour and cook for 1 minute. Stir in broth, wine, and soy sauce, scraping up any browned bits. Bring to simmer and cook, stirring occasionally, until mixture has thickened slightly, 1 to 2 minutes. Stir in peas and remove from heat.
- Adjust oven rack 5 inches from broiler element and heat broiler. Using spoon, dollop potato mixture evenly over filling and smooth into even layer. Pressing gently, drag tines of fork across surface of potato mixture to make ridges. Transfer skillet to oven and broil until topping is golden brown, 5 to 7 minutes. Let cool for 10 minutes. Serve.
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