Boil the noodles: Cook the lasagna noodles in salted boiling water until just al dente, about 1 minute less than the package suggests. Drain and lay flat on a sheet of parchment paper to prevent sticking.
Build the sauce base: Heat the olive oil in a large skillet over medium heat. Add the garlic and sun-dried tomatoes, cooking for 1 minute until fragrant. Stir in the tomato paste and cook for another minute to deepen its flavor.
Add the liquid and go a little thinner than instinct says to: Pour in the chicken broth and heavy cream, whisking to combine, along with the Italian seasoning and red pepper flakes. This lasagna needs a noticeably thinner sauce than the original stovetop version of Marry Me Chicken, since the noodles will absorb a good amount of liquid while baking a sauce that seems perfectly saucy going into the oven often turns dry and pasty by the time the lasagna finishes, so err toward slightly thin rather than thick at this stage.
Simmer and add the chicken: Let the sauce simmer for 5 minutes to reduce slightly, then stir in the shredded chicken and remove from heat.
Make the ricotta mixture: In a mixing bowl, combine the ricotta, egg, ½ cup of the parmesan, and the chopped spinach until evenly mixed.
Layer the lasagna: Preheat the oven to 375°F. Spread a thin layer of sauce in the bottom of the baking dish, then layer noodles, a portion of the ricotta mixture, a portion of the chicken sauce, and a sprinkle of mozzarella. Repeat the layers, finishing with a generous top layer of mozzarella and the remaining parmesan. Pro tip: save a little extra sauce to pour over the very top layer of noodles before the final cheese dry-looking edges on the top noodles are a common giveaway of an underbaked, chewy corner piece.
Bake covered, then uncovered: Cover the dish tightly with foil and bake for 25 minutes. Remove the foil and bake for another 15–20 minutes, until the top is golden and bubbling at the edges.
Rest before slicing: Let the lasagna rest for 10 minutes before cutting this helps the layers hold together instead of sliding apart on the plate.