How to Make It
Bring vegetable broth to a boil in a medium saucepan over high. Reduce heat to medium, and simmer until reduced to 2 cups, 8 to 10 minutes.
Bring wine to a boil over high in a small saucepan until reduced to 1 cup, about 5 minutes. Stir wine into vegetable broth, and cover to keep warm.
Preheat oven to 350°F. Using a sharp knife, cut round ends from each squash and reserve for another use. Peel and cut remaining squash into 6 (4 1/2- x 1 1/2-inch) rectangles; sprinkle with salt and pepper.
Heat oil in a large skillet over medium-high. Cook squash in batches until golden brown on both sides, about 4 minutes on each side. Transfer to a plate.
Add diced tomatoes, leeks, carrots, onion, and garlic cloves to skillet over medium-high. Cook, stirring often, until tender and slightly browned, about 6 minutes. Stir broth mixture into tomato mixture.
Transfer tomato-broth mixture to a 13x9-inch baking dish. Add parsley, thyme, rosemary, and bay leaf. Nestle butternut planks into mixture; cover dish with parchment paper, and seal tightly with aluminum foil. Bake until squash is tender, about 1 hour and 15 minutes.
Remove foil and parchment paper, and transfer squash to a serving platter. Pour braising liquid through a fine mesh strainer into a small saucepan; discard solids. Bring strained liquid to a boil in saucepan over medium-high, whisking constantly for 5 minutes. Spoon sauce over squash; drizzle with olive oil. Serve with creamy grits and broccolini, if desired.