Step 1

If you'd like a browned lasagna top, heat the oven to broil and use an oven-safe skillet.

Step 2

Heat the oil in a 12-inch or larger regular or cast iron skillet over medium-high heat until shimmering. Add the onion and sausage and cook, breaking the meat up into small pieces with a wooden spoon, until the sausage is cooked through, about 6 minutes. Add the mushrooms and sauté until tender, about 5 minutes.

Step 3

Add the marinara and broth, stir to combine, and bring to a simmer. Using your hands, break the lasagna noodles into 1 1/2- to 2-inch pieces and add to the pan. Stir to combine and spread into an even layer, making sure as many of the noodles are submerged in liquid as possible. Reduce the heat to medium and simmer briskly uncovered (small bubbles all over), stirring occasionally, until the noodles are just tender and the sauce has thickened slightly, about 25 minutes (add water 1/4 cup at a time as needed if the noodles have absorbed all the liquid before they're cooked). Make sure the noodles are always submerged in sauce.

Step 4

A minute or 2 before the noodles are ready, dollop the cottage cheese over the lasagna with a small spoon and do not stir anymore. Taste and season with salt as needed.

Step 5

Remove the pan from the heat and sprinkle with the mozzarella and Parmesan. Cover and let sit until the cheese is melted, about 5 minutes. (Alternatively, for a browned top, place the pan under the broiler for a few minutes until the cheese is golden-brown in spots.) Sprinkle with the parsley if using and serve.