MAKE THE CARROT-CAULIFLOWER LAYERS. Place the carrots and cauliflower in the bowl of a food processor fitted with a steel chopping blade. Process until smooth. In a large skillet, heat the oil over medium-high heat. Add the onions and saute them until tender and golden. This will take about 5 minutes. Stir in the butter and let it melt. Scrape the onions and butter into the processor. Add all the remaining ingredients for the carrot-cauliflower layers and process until smooth. Scrape into a bowl, cover, and refrigerate while preparing the other layer. Preheat your oven to 350F. Bring a large pot of water to a boil. Butter a 9-by-5-by-3-inch loaf pan. Line the bottom and ends with buttered wax paper, buttered side up.
MAKE THE SPINACH-MUSHROOM LAYER. Place the spinach in the processor and pulse a few times. Cook the onions in hot oil for 1 minute. Add the frozen mushrooms and cook them along with the onions over high heat until all the liquid has evaporated, about 6 to 7 minutes. Stir in the butter. Scrape the mixture into the processor. Add all the remaining ingredients and process until smooth. Scrape about half of the carrot-cauliflower mixture into the pan, packing it well into the corners, and flattening it with a spatula or the palm of your hand to remove any air pockets. Add all of the spinach-mushroom mixture, and again flatten it. Finally, add the remaining carrot mixture. Smooth it down on top. Cover with buttered wax paper. Place pan in another pan and fill the latter with boiling water to a level of 2 inches up the side of the terrine. Bake in the preheated oven for 1 1/4 hours, or until a knife inserted into the middle comes out clean. Remove terrine from the oven and cover it with a piece of cardboard or a second loaf pan (the same size) right side up. Place about 1 pound of weight, evenly distributed, on the terrine. Refrigerate until well chilled, at least 2 hours. Once chilled, carefully remove from the pan by running a thin-bladed knife between the terrine and the pan. Invert onto a flat dish, peel off the paper and serve. Garnish with curly leafed lettuce, if desired.