Preheat the Broiler
Set the oven broiler to preheat with the rack positioned 5 inches from the heat source.
Cook the Spinach
Heat olive oil in a 10-inch broiler-safe skillet over medium-high heat. Add the spinach in two batches, tossing constantly until wilted (about 2 minutes per batch). Transfer to a bowl and set aside.
Make the Sauce
Lower the heat to medium and melt the butter in the skillet. Add the flour and whisk continuously for 2 minutes until the mixture turns light brown. Gradually whisk in warmed milk, cooking for 3–4 minutes until the sauce thickens. Stir in pesto and kosher salt.
Combine Spinach and Pasta
Return the cooked spinach to the skillet, stirring it into the sauce. Add 3/4 cup of water to loosen the mixture. Using tongs, submerge the broken lasagna noodle pieces into the sauce. Bring to a boil, reduce the heat to medium-low, cover, and simmer for 14–15 minutes, or until noodles are tender.
Prepare the Ricotta Mixture
In a small bowl, mix ricotta cheese with lemon zest.
Assemble the Lasagna
Once the noodles are cooked, dollop the ricotta mixture over the pasta. Sprinkle grated mozzarella evenly over the top.
Broil to Finish
Transfer the skillet to the preheated broiler. Broil for about 2 minutes, or until the cheese is melted and golden brown.
Garnish and Serve
Remove from the oven, top with fresh basil leaves, and serve hot.