This recipe goes more smoothly if you prep/lay out all the ingredients ahead of time. Start by thawing the spinach and microwaving the cream cheese for about 30 seconds or until it's very soft (this is important so it melts into the sauce easily).
Preheat your oven to 375F and move the rack to the top third of the oven.
Boil a large, salted pot of water for the lasagna noodles. Cook them al dente (about 7-8 minutes). Be careful not to overcook them. Stir them occasionally to prevent sticking. Once they're cooked, drain them (do not rinse). When they're cool enough to handle after a couple of minutes, lay them out individually on a sheet of parchment paper so they don't stick together.
Meanwhile, add the egg to a fairly large prep bowl and beat it with a fork. Add in the remaining cheese mixture ingredients and stir until well combined.
Make the cream sauce: add the butter and onion to a skillet and sauté for 4-5 minutes over medium heat. Stir in the garlic and cook for about 30 seconds, then add in the cream cheese, cream, and salt & pepper. Stir/whisk until the cream cheese has melted in. This process should take about 5 minutes. Do not let the sauce get too thick. It should have a similar consistency to Alfredo sauce, and it will thicken more once you take it off the stove and then as it cooks in the oven. Add a splash more cream to thin if needed.
To assemble the lasagna: spread some of the cream sauce on the bottom of a deep 9x13 casserole dish (about 1/4 cup sauce). Add 4 noodles to the bottom of the casserole dish (they will overlap a bit). Spread 1/2 of the cheese mixture over top, add 1/2 the chicken, and then spoon about 1/3 of the cream sauce on top of that. Add another 4 noodles, the rest of the cheese mixture, the rest of the chicken, another 1/3 of the cream sauce, and then the final layer of 4 noodles. Spread on the rest of the cream sauce, then top with the remaining 2 cups of mozzarella cheese.
Cover with foil and bake for 30 minutes, then uncover and continue baking for another 15 minutes. If needed, broil for a few minutes until the cheese is browned (watch it carefully).
Let the lasagna sit for 10 minutes before slicing. I recommend slicing it into squares with a sharp knife then scooping each piece out with a spatula. Season with extra salt & pepper as needed.