Before you begin, make sure to THAW and DRAIN the spinach thoroughly. This can take some time so plan ahead. I like to leave it in the boxes, place the boxes in warm water for a while, then pour it all into a colander and place something heavy on top.
PLACE MUSHROOMS in a large (6 to 8 quart) saut pan on high or medium high heat, STIRRING or shaking frequently. You may hear them squeak. ADD SALT evenly. The mushrooms will sizzle and then start to release water. (Note that you are not adding fat at this point to the pan; this method of cooking mushrooms in their own moisture is called "dry sauting.) Once the mushrooms start to release water into the pan, STIR IN the chopped onions. Cook until the mushrooms are no longer releasing moisture and the mushroom water has boiled away, about 5-10 minutes more.
ADD the olive oil to the mushrooms and stir to coat. SAUTE the mushrooms and onions for about a minute. ADD the garlic and cook for another minute. STIR IN the tomato paste, cook for a minute longer. RESERVE 1 cup of the tomato sauce (it will go in the bottom of the casserole dish), and POUR the remaining cup of tomato sauce into the mushrooms along with the crushed tomatoes, and one cup of water. STIR IN the thyme, sugar, dried basil and red pepper flakes. Bring to a simmer, then lower the heat and continue to SIMMER for 20 minutes.
PREHEAT the oven to 350F.
SPREAD the one cup of reserved tomato sauce over the bottom of a large (preferably 10x15-inch) casserole dish. (If your casserole dish is smaller, you may need to add another layer as you go through this step.) PLACE a layer of lasagna noodles down over the tomato sauce, slightly overlapping. (For our 10x15-inch dish, we ultimately fit 3 layers of noodles, each layer with 6 noodles.) SPRINKLE half of the ricotta cheese over the noodles. SPRINKLE half of the drained spinach over the ricotta. SPRINKLE half of the Mozzarella cheese over the spinach, and just a quarter of the pecorino cheese. Then SPOON 1/3 of your mushroom sauce over the Mozzarella. SPRINKLE half of the fresh basil over the sauce if using.
REPEAT the layering process. Place a second LAYER of noodles over the sauce. SPREAD the remaining ricotta, spinach, and Mozzarella over the noodles. SPRINKLE another quarter of the pecorino along with the Mozzarella. TOP with another third of the mushroom sauce and the remaining fresh basil. LAYER your final layer of lasagna noodles over the sauce. SPREAD the remaining mushroom sauce over the lasagna noodles, and SPRINKLE with the remaining pecorino or parmesan cheese. TIP: Be sure to cover the noodles completely with sauce, don't leave them exposed or the oven will dry them out around the edges.
SPREAD a little olive oil over the inside of a piece of aluminum foil, then COVER the casserole dish and crimp the edges. BAKE at 350F for 25 minutes, then remove the foil and bake uncovered for an additional 25 minutes.
Let the lasagna cool for 10 minutes before cutting to serve.