FOR PASTA: Trim stems from spinach and rinse leaves in several changes of cold water; do not dry. Put wet spinach leaves in a medium saucepan with pinch salt; cook, covered, over medium heat until tender, 3 to 5 minutes. Drain spinach and let cool, then squeeze out excess liquid and very finely chop.

On a clean work surface, mound flour and form a well in the center. Add spinach, egg, oil and pinch salt
to the well. Using a fork, gently break up yolk and slowly incorporate flour from inside rim of well. Continue until liquid is absorbed. When dough becomes too stiff to work with a fork, knead by hand until flour is fully incorporated, adding additional flour in 1 tablespoon increments if dough is sticky (any stickiness will depend on how well spinach was squeezed). Wrap dough tightly in plastic and let rest at room temperature for 30 minutes. While pasta rests, prepare filling.  

FOR FILLING: Bring a medium saucepan of water to a boil. Add beans and cook for 1 minute; immediately transfer with slotted spoon to a bowl of ice water to stop cooking (reserve cooking liquid). Drain beans, then gently peel and discard skins. 

In a medium skillet, heat 2 tablespoons oil over medium heat. Add leeks and generous pinch salt, reduce heat to low and cook, stirring frequently, until leeks are tender, about 20 minutes.

Meanwhile, heat remaining 2 tablespoons oil in a 12-inch skillet over medium-high heat. Add carrots; cook 2 minutes, then add broth. Gently simmer carrots in broth 10 minutes, then add zucchini and cook 2 minutes more. Add beans, generous pinch pepper and  1/2 teaspoon salt. Continue to cook until vegetables are tender, about 3 minutes more. Remove from heat. Transfer carrot mixture, including liquid in pan, to a bowl; add leeks and gently stir to combine.

Bring a large wide pot of salted water to a boil. Meanwhile, cut pasta dough into 2 pieces. Flatten 1 piece so that it will fit through the rollers of a pasta machine. Set rollers of pasta machine at the widest setting, then feed pasta through rollers 3 or 4 times, folding
and turning pasta until it is smooth and the width of the machine. Roll pasta through machine, decreasing the setting one notch at a time (do not fold or turn pasta), until pasta sheet is scant 1/16 inch thick. Cut sheet into rectangles, about 7 inches long and the width of the pasta roller. Lay lasagna sheets on a lightly floured baking sheet in a single layer between very lightly floured pieces of parchment or waxed paper until ready to use. Repeat with second piece of dough.

Set a large bowl of ice water adjacent to stove. Add lasagna sheets, a few at a time, to the boiling water. Cook for about 15 seconds. Immediately remove with a slotted spoon and transfer to ice water to keep from overcooking. Drain well.

FOR BÉCHAMEL: In a medium saucepan, heat milk over medium-low heat; bring just to a boil and remove
from heat. In large saucepan, melt 4 tablespoons butter over low heat. Add flour and cook, stirring constantly with a wooden spoon, 2 minutes. Do not brown. Remove from heat.

Add about 2 tablespoons of the warm milk to flour mixture, stirring constantly until milk is incorporated. Repeat until about  1/2 cup of the milk has been added, incorporating between additions, then, in a slow and steady stream, whisk in remaining milk. Bring mixture to a gentle simmer and cook, stirring frequently, especially into edges of pan, until sauce is the consistency of a thick cream, about
5 minutes more. Add remaining tablespoon butter and 1 teaspoon salt; stir to combine. Remove from heat.

Grease an 11- x 7- x 2-inch baking dish with butter. Lightly pat dry lasagna sheets with a clean kitchen towel to absorb excess moisture.

Spread 2 tablespoons of the béchamel on the bottom of baking dish. Top with a layer of lasagna sheets, overlapping the noodles slightly and letting excess hang up and over sides of pan. Cover with 1/5 of the béchamel and cheese and 1/4 of the vegetable filling. Top with another layer of pasta, trimming noodles, if necessary, to fit the dish. Top with another layer of filling, béchamel and cheese. Repeat two more times, then fold any overflowing pasta over the dish. Top with the remaining béchamel and cheese. Bake lasagna until heated through and bubbly, about 20 minutes. Let rest 5 to 10 minutes before slicing.

Note: Stracchino cheese (also known as Crescenza) can be purchased at Italian markets, or by mail order from Buon Italia, buonitalia.com; (212) 633-9090.

Photo by Ellen Silverman

Food styling by Maggie Ruggiero; prop styling by Amy Wilson