Instructions

1. Bring a large pot of water to a boil. Add spinach; cook until tender, 4-5 minutes. Drain. Squeeze liquid from spinach; chop very finely. Wrap spinach in a towel; squeeze to dry completely (you should have 3⁄4 cup).
2. Make the pasta: Combine spinach, eggs, and 1 tbsp. water in a bowl; mix with a fork. Mound 2 1⁄2 cups flour on a work surface; create a wide well in center with your hands. Sprinkle 1 tsp. salt over flour. Pour spinach mixture into well and, using a fork, begin to slowly incorporate flour from well into spinach mixture, using a circular motion, to make a stiff dough. Knead dough, adding a little flour as necessary to prevent sticking, until it is smooth and elastic, about 10 minutes. Wrap dough in plastic wrap; let rest for 30 minutes.
3. Divide dough into 6 pieces; cover all but 1 piece with a towel. Using your hands, flatten the piece of dough into a rectangle. Pass dough through widest setting of a hand-cranked pasta roller. Fold dough into thirds to create another rectangle; pass dough through widest setting again, feeding open edge through first; fold into thirds again and roll twice through same setting. Decrease setting one notch; roll pasta through to make a thinner pasta sheet. Lower setting again; feed pasta sheet through roller. Repeat through each setting until very thin, about 1⁄16", stopping at the second-to-last setting. Halve pasta sheet crosswise and transfer to a parchment paper-lined sheet tray; dust lightly with flour. Repeat above steps with remaining dough pieces, layering sheets between pieces of floured parchment paper.
4. Bring a large pot of salted water to a boil. Add roughly a quarter of the pasta sheets, stir gently, and cook until just al dente, 2-3 minutes. Using a slotted spoon, remove pasta sheets and lay flat on a damp towel without overlapping; cover with another damp towel. Repeat with remaining pasta.
5. Make the besciamella sauce: Heat 3 tbsp. butter in a saucepan over medium-low heat. Whisk in remaining flour and cook, whisking constantly, until it begins to bubble, about 3 minutes. While whisking, add milk in a steady stream. Bring to a simmer and cook, whisking occasionally, until sauce thickens, 10-15 minutes. Season generously with salt and pepper and set besciamella aside.
6. Assemble the lasagne: Heat oven to 450°. Spread 1 cup ragu over bottom of a 2-quart baking dish, then cover evenly with 2 sheets of pasta, cutting to fit. Top with 3⁄4 cup ragu, spread with 1⁄4 cup besciamella, then sprinkle with 1⁄4 cup cheese. Starting with another layer of pasta, repeat layering process 3 more times. Top with another pasta layer (don't trim edges), remaining besciamella, and cheese; dot with remaining butter. (Reserve any remaining pasta for another use.) Bake for 15 minutes; reduce heat to 350°. Continue baking until bubbly, 15-20 minutes more. Let cool slightly before serving.