Fill a pot 3/4 the way with water. Season with 2 tbsp of salt and bring to a boil. Cook the lasagna noodles according to package and remove. Run under cold water & toss in olive oil to prevent sticking. Place on a sheet pan.
Cook the squash in the same pot for 10-15 minutes, until soft. Drain and set aside.
Heat the pot on medium heat. Season with olive oil. Add onion, sage and leeks and cook for 5-7 minutes, until the onions are translucent. Add garlic & cook 1 minute, until fragrant. Add spinach, a generous pinch of salt and the nutmeg and mix until spinach is bright green and wilted (2 minutes or so.)
Preheat the oven to 375 F.
Pour squash into the pot with goat cheese and mash with a whisk until creamy. Add balsamic and another pinch of salt. Taste for seasoning and adjust if necessary. Add some grated Parm (I did about 1/4 cup) and ~1 cup of mozzarella and stir until the cheese is melted. Remove the filling from the heat.
Place lasagna noodles on a clean workspace. Using a spoon, spread the filling onto the noodle - about 1/2 inch thick- then roll it up. Repeat. If you have leftover filling, layer it on the bottom of a baking dish. If you don’t, just sprinkle 1/2 cup mozzarella on the bottom of a baking dish. Place the roll ups into the dish. Top with more cheese if desired. Bake for 20 min.
While it’s cooking, brown the butter.
Just before serving, pour brown butter and balsamic onto the finished lasagna.