Vegetarian Shepherds Pie

Name: Vegetarian Shepherd's Pie
Ingredients: 3 lb russet potatoes, peeled and quartered; Kosher salt, to taste; 1 lb sweet potatoes, peeled and quartered; 1/3 cup milk, heated; 1/2 cup grated parmesan, plus more; 2 tbsp unsalted butter; freshly ground black pepper, to taste; 1 tbsp olive oil; 2 cloves of garlic, minced; 1 medium onion, diced; 14 oz portobello mushrooms, diced; 1 tbsp chopped rosemary; 2 tbsp tomato paste; 1 qt mushroom broth; 1 cup french green lentils; 1 bay leaf; 1/2 lb brussels sprouts, quartered; 1/2 lb each parsnips, carrots, and turnips, peeled and cut into 1 pieces; 2 sprigs of thyme