Preheat the oven to 375°F (190°C). Add the 3 pounds of potatoes to a large pot of salted water and boil for 20-25 minutes or until fork-tender.

In a small saucepan, combine the ½ cup milk, 4 tablespoons butter, 1 garlic clove, and 1 sprig rosemary. Bring to a simmer, then turn off the heat and set aside.

While the potatoes are boiling, melt the 2 tablespoons butter in a shallow Dutch oven or 12-inch oven-safe pan over medium heat. Add the chopped carrots, celery, and onion along with a pinch of salt. Sauté for 7 minutes, stirring occasionally, until the vegetables are tender. Add the 3 minced garlic cloves and sauté for 2 minutes. Add the ground lamb, ½ teaspoon kosher salt, minced rosemary, and crushed fennel seeds. Cook for about 5 minutes or until the meat is fully cooked. Pour in the ½ cup white wine and add another pinch of salt. Let the wine evaporate, about 5 minutes. Taste the mixture and adjust salt as needed. Turn off the heat.

When the potatoes are done, drain them well. Process the potatoes through a ricer for a smooth texture or use a potato masher if you prefer some texture. Remove the rosemary and garlic from the milk mixture. Pour the warm milk mixture into the potatoes and add 2 to 3 pinches of salt. Mix until smooth and creamy. Taste and adjust seasoning if needed.

Flatten the lamb mixture evenly in the pan. Spread the mashed potatoes on top, smoothing them out with a spatula. Sprinkle the 1 cup grated Gruyère cheese evenly over the top.