Beef and Spinach Shepherd's Pie

Place potatoes in a medium saucepan and cover with cold water. Season with salt. Bring to a boil, then reduce heat and simmer until tender, 12 to 15; drain and return to pan. Meanwhile, in a large skillet over medium-high heat, brown beef, breaking it up with a wooden spoon, 5 minutes. Add onion, carrots, celery, garlic, thyme, and rosemary and cook until vegetables are soft, 5 minutes. Spoon out and discard any extra grease in pan and season with salt and pepper. Stir in tomato paste and chicken broth; let simmer until liquid reduces slightly, 3 to 4 minutes. Stir in spinach until wilted, 2 to 3 minutes. Preheat broiler to high. Add milk to drained potatoes and bring to a simmer. Using a potato masher or fork, mash potatoes until smooth. Stir in olive oil and season with salt and pepper. Spoon beef and spinach mixture into a medium-sized baking dish and spoon mashed potatoes on top. Use a fork to create texture on top (the potatoes will brown better) and drizzle with olive oil. Broil until nicely browned on top, 2 to 3 minutes. Serve immediately with a green salad.