Preheat oven to 325 degrees. Split the acorn squashes down the middle and remove seeds. Place squashes in a deep roasting pan, cut side down, add 1 cup of water, cover the pan with foil and roast until the squash is tender but the skin is still intact.
Remove squash from oven. Carefully spoon out the meat of the squash and transfer to a separate bowl taking care to leave the skin intact. Set skins aside. In a large saucepan combine oil, onions, ginger and garlic, and sauté over medium heat. Once onions and garlic have begun to break down and become translucent, add the butter and turn the heat to low. Add the kaffir lime leaves and all of your squash. Cook the squash mixture for 20 minutes and then remove from the stovetop.
Transfer squash mixture into a blender and purée until smooth. Season to taste with salt and pepper and portion purée equally into squash skins and increase oven to 350 degrees.
Before serving, carefully place the squashes on baking sheet and transfer to oven for 5 minutes or until heated through. In a large mixing bowl toss the greens with brown butter, lemon juice, lemon zest and season to taste with salt and pepper. Top squash halves with greens, garnish with cheese, pumpkin seeds and lemon zest and serve.