Preheat the grill to medium-high heat. In a small bowl, mix olive oil, salt, black pepper, and fresh rosemary. Rub this mixture all over the rack of lamb and let it marinate for at least 30 minutes.

Grill the Lamb

Place the marinated rack of lamb on the grill and cook for about 15-20 minutes, turning occasionally, until the internal temperature reaches 130°F (medium-rare). Remove from the grill and let it rest for 10 minutes before slicing.

Making the Rosemary Sauce

Prepare the Sauce

In a saucepan over medium heat, pour in the red wine and bring it to a simmer. Add fresh rosemary and beef stock, reducing the mixture by half. Whisk in the butter until melted and smooth.

Making the Aligot Purée

Prepare the Potatoes

Peel and boil the potatoes until tender. Drain and return to the pot.

Mix the Purée

Add heavy cream, grated cheese, butter, and salt to the potatoes. Mash until smooth and creamy, stirring until the cheese is fully melted and incorporated.

Cooking the Rapinis

Sauté the Rapinis

In a skillet, heat olive oil over medium heat. Add minced garlic and sauté for about 1 minute. Add the rapini and cook until tender, about 3-5 minutes. Season with salt to taste.

Sautéing the Mushrooms

Cook the Mushrooms

In another skillet, heat olive oil over medium heat. Add sliced mushrooms and cook until browned and tender, about 5-7 minutes. Season with salt and black pepper to taste.