Bring a large pot of salted water to a boil. Cook the lasagna noodles according to package directions. Drain, toss with olive oil, and reserve.
Preheat oven to 350ºF. Place the spinach in a large pan over medium heat. If spinach is still wet, simply cover pan and wilt. If it’s dry, add ¼ cup water to the pan, cover, and wilt. Drain spinach. When cool enough to handle, roughly chop it and squeeze out excess liquid.
Place spinach in a large bowl with the ricotta, eggs, garlic, zest, nutmeg, peas, asparagus, Parmigiano and half of the mozzarella. Season to taste with salt and pepper.
Place half the noodles along the bottom of a 9” x 13” pan. Top with half of the ricotta mixture. Repeat with remaining noodles and ricotta mixture.
Strew remaining mozzarella over the top. Place in the oven and cook until heated through (about 30 minutes).