Get started by preheating your oven to 350°F. Toast pecans on a rimmed baking sheet, tossing once, until fragrant and slightly darkened, 10–15 minutes. Let cool, then coarsely chop and set aside.
Increase your oven temperature to 400°F. Prepare a rimmed baking sheet with aluminum foil.
Find your zucchini, and cut in half lengthwise. Use a spoon or ice-cream scoop to scoop out insides, leaving a small divot down the center. Reserve zucchini filling aside.
Cut eggplant in half lengthwise and scoop out insides, leaving a 1/4″ border on all sides and creating a divot deep enough to fit zucchini halves inside. Reserve eggplant filling.
Cut butternut squash in half lengthwise and remove seeds. Scoop out insides, leaving a 1/2″ border on all sides and creating a divot deep enough to fit eggplant halves inside. Reserve squash filling.
Use a fork to pierce the insides of the squash and zucchini halves. Use a sharp knife to make shallow crosshatch marks inside of the eggplants. Be careful not to pierce the skin! Trim scallions to match the length of the squash.
Coarsely chop 1 garlic clove. Combine chopped garlic, shallot, mushrooms, zucchini filling, eggplant filling, and squash filling in a large bowl. Pulse the contents of the bowl in the blender until finely chopped. You may need to do this in batches.
Heat oil over medium in a large skillet. Add the vegetable purée and 3 thyme sprigs. Cook, stirring occasionally, until mixture begins to brown, about 5 minutes. Return to bowl and let cool.
Meanwhile, chop remaining garlic clove and combine with butter, red pepper flakes, and remaining 6 thyme sprigs in a small pot. Cook over medium heat, stirring occasionally, until butter is melted, then stir in maple syrup.
Pluck out thyme sprigs from vegetable mixture. Stir in the eggs, Parmesan, breadcrumbs, 3 Tbsp. parsley, and 1 tsp. salt.
Place squash halves, cut side up, on prepared baking sheet. Brush inside of each with maple syrup butter and season with 1/2 tsp. salt. Using the back of a spoon, press 3/4 cup vegetable mixture into each half until interior is fully coated. Sprinkle with 1/4 cup reserved pecans.
Now try to fit the eggplant halves, cut side up, inside of the squash halves. Brush inside of each eggplant half with maple syrup butter and season with 1/2 tsp. salt. Using the back of a spoon, press 1/3 cup vegetable mixture into each half until interior is fully coated. Sprinkle with 1/4 cup pecans.
Now nestle zucchini halves, cut side up, inside eggplant halves. Brush inside of each zucchini half with maple syrup butter and season with 1/8 tsp. salt. Using a spoon, fill zucchini halves with 1/4 cup vegetable mixture, spreading it flat. Sprinkle with 1/4 cup pecans (reserve remaining pecans), then lay scallions down the middle.
Cut 3 lengths of kitchen twine. Slip twine under one squash half, then top with second squash half, so that cut sides face each other, and press down to seal. Tightly tie twine around squash to secure. Brush top with maple syrup butter (reserve remaining butter) and season with 1/2 tsp. salt. Wrap squash in aluminum foil and place in the center of the baking sheet. Using 2 loaf pans or small metal bowls turned upside down, keep squash secure on baking sheet.
Bake until squash is tender to the touch, 1 hour 45 minutes–2 hours. Remove foil and let rest 20 minutes.
Meanwhile, pick out the thyme from remaining maple syrup butter, heat over medium-low until warm, then stir in mint, lemon juice, 1 tsp. salt, and remaining 3 Tbsp. parsley.
Place the Vegducken on a cutting board and cut into 1″ slices with a serrated knife, transferring to serving plates as you go. Spoon herb butter over slices, garnish with remaining pecans, and serve.