Step 1

Blend all ingredients in processor until coarse puree forms. Season with salt and pepper.

Step 2

Melt butter in heavy large saucepan over medium heat. Add shallots; sauté 2 minutes. Add flour; whisk until smooth. Reduce heat to low; whisk 1 minute. Gradually whisk in milk. Bring to boil, whisking constantly. Add bay leaf. Reduce heat; simmer until slightly thickened, stirring often, about 5 minutes. Mix in nutmeg. Season with salt and pepper. Cool sauce slightly.

Step 3

Butter 13x9x2-inch baking dish. Cook noodles in pot of boiling water until just tender but still firm to bite. Drain. Rinse under cold water; drain.

Step 4

Mix 1 cup pesto and broth in small bown (reserve remaining pesto for another use). Spread 1/2 cup béchamel sauce over bottom of prepared dish. Overlap 4 noodles atop sauce to cover. Spread 1 cup béchamel sauce over. Spoon 1/3 of pesto over. Sprinkle with 1/3 cup Parmesan. Repeat layering twice, using 4 noodles. 1 cup béchamel, 1/3 of pesto and 1/3 cup cheese for each layer. Cover with 4 noodles. Spread remaining béchamel over. Sprinkle with 1/3 cup Parmesan. DO AHEAD Can be made 1 day ahead. Cover; chill.

Step 5

Preheat over to 375°F. Cover lasagne loosely with foil. Bake 30 minutes (if refrigerated, bake 45 minutes). Uncover and bake until bubbling, about 20 minutes. Let stand 15 minutes. Cut into squares.