Eggplant Shepherds Pie

Name: Eggplant Shepherd's Pie
Ingredients: 3 tablespoons olive oil; 1 medium eggplant, peeled and chopped; 2 cups frozen pearl onions, thawed; 2 carrots, chopped; 2 cups vegetable broth; 2 tablespoons tomato paste; 2 tablespoons chopped fresh flat-leaf parsley, plus more for garnish; ½ teaspoon black pepper; 1 teaspoon kosher salt, divided, plus more for cooking potatoes; 2 medium russet potatoes, peeled and chopped; 2 ounces pecorino cheese, grated (about 1/2 cup); ½ cup whole milk