Vegetable Shepherd's Pie

INGREDIENTS

• 1 1/2-2 cups whole milk, warmed
• 1 cup frozen pearl onions, thawed, halved
• Freshly ground black pepper
• 2 tablespoons gluten-free white miso or 2 teaspoons gluten-free tamari soy sauce
• 2 cups dry white wine
• 5 tablespoons olive oil, divided
• 2 cups bite-size pieces mixed fresh mushrooms
• 2 4" rosemary sprigs
• 2 bay leaves
• 3/4 cup brown or French green lentils
• 3 pounds Yukon Gold potatoes, unpeeled
• 3 pounds russet potatoes, unpeeled
• 2 tablespoons tomato paste
• Kosher salt
• 8 cups vegetable broth
• 6 garlic cloves, divided, plus 2 tablespoons chopped garlic
• 1/4 cup chopped mixed fresh herb (such as parsley, chives, and sage)
• 1/2 cup (1 stick) unsalted butter, cut into 1/2" cubes
• 12 cups 1/2" pieces peeled fall vegetables (such as squash, turnips, carrots, and parsnips)
• 3 cups coarsely chopped onions
• 1 teaspoon kosher salt plus more
• 1 ounce dried porcini mushrooms
• 2 tablespoons cornstarch