Crisp, golden potato tots take the place of mashed potatoes in this otherwise traditional cottage pie. Baking the tots before adding to the top of the skillet ensures that they remain crisp after their second bake.
Preheat the oven to 400˚ F. Spread the potato tots in an even layer on a baking sheet. Bake until lightly golden and starting to crisp, 15 to 18 minutes.
Meanwhile, heat the olive oil in a 10-inch ovenproof skillet over medium-high heat. Add the white and light green parts of the scallions, the carrot and 1/2 teaspoon each salt and pepper. Cook until the carrot is crisp-tender, about 5 minutes. Add the garlic and thyme and cook until the garlic begins to soften, about 1 minute.
Make a large well in the center of the vegetables and add the beef. Cook the beef, breaking it up with a wooden spoon, until browned all over, about 6 minutes. Stir in the tomato paste until well combined, then stir in the flour until the beef is coated. Add the beef broth and green beans and bring the mixture to a boil, then reduce the heat to a simmer and cook until the mixture has thickened to a stew-like consistency, about 10 minutes.
Remove the beef mixture from the heat and arrange the potato tots on top in an even layer. Transfer the skillet to the oven and bake until the mixture bubbles and thickens, 8 to 10 minutes. Switch the oven to broil and broil the top of the pie until deep golden and crisp, 2 to 3 minutes. Sprinkle with the dark scallion greens.