Hachis Parmentier

Name: Hachis Parmentier
Ingredients: 3 pounds russet potatoes; Kosher salt and freshly cracked black pepper; 1/2 cup sour cream; 2 sticks unsalted butter, melted; 2 large egg yolks; 1/4 cup chopped fresh parsley; 1/2 cup whole milk, warmed, as needed; 1/2 cup grated Parmesan; 4 tablespoons unsalted butter; 1 large carrot, small diced; 1 medium parsnip, peeled and small diced; 1 medium stalk celery, small diced; 1/2 large white onion or 1 small white onion, small diced; Kosher salt and freshly ground black pepper; 3 small or 2 large cloves garlic, minced; 2 tablespoons tomato paste; 2 pounds (75/25%) ground chuck; 1 tablespoon chopped fresh thyme; 1 teaspoon dried thyme; 1/2 cup red wine (one that you like to drink); 2 to 3 teaspoons red wine vinegar; 1/2 cup chopped fresh parsley, plus more for garnish; 1/4 cup grated Parmesan