Step 1

Bring a large pot of salted water to a boilover high. Fill a large bowl with ice water; place clean kitchen towels on work surface. Hold each pasta sheet at 1 end with both hands, and slowly lower into boiling water. Repeat with 4 pasta sheets; cook, stirring gently, until al dente, about 30 seconds. (If using dried pasta, cook according to package directions for al dente.) Remove from water using a spider or kitchen tongs, and submerge in ice water 30 seconds. Remove from ice water, and lay flat on kitchen towels. (Do not stack.) Smooth out pasta using your hands. Repeat with remaining pasta sheets.

Step 2

Preheat oven to 375°F. Grease inside of a deep 13- x 9-inch baking dish with butter. Spread 3/4 cup béchamel on bottom of prepared dish.

Step 3

Top with 2 pasta sheets, covering bottom of dish completely, pushing any overlap up sides. Spread with 1 cup béchamel; top with 1 2/3 cups ragù. Sprinkle with 1/3 cup grated Parmesan. Top with 2 pasta sheets. Spread with 1 cup béchamel. Top evenly with half of prosciutto. Sprinkle with 1 1/3 cups fontina and 1/3 cup grated Parmesan.

Step 4

Top with 2 pasta sheets. Spread with 1 cup béchamel; top with 1 2/3 cups ragù. Sprinkle with 1/3 cup grated Parmesan. Top with 2 pasta sheets. Spread with 1 cup béchamel. Top with remaining prosciutto. Sprinkle with 1 1/3 cups fontina and 1/3 cup grated Parmesan. Top with 2 pasta sheets. Spread with 1 cup béchamel; top with 1 2/3 cups ragù. Sprinkle with 1/3 cup grated Parmesan. Top with 2 pasta sheets. Spread with remaining béchamel, and sprinkle with remaining fontina and remaining Parmesan.

Step 5

Cover lasagna with aluminum foil. Bake on a rimmed baking sheet on middle rack in preheated oven 55 minutes. Remove foil; bake until top is golden brown, about 35 minutes. Remove from oven; let rest at least 30 minutes before serving.