For the pesto: Combine half pesto ingredients in a blender or food processor, and process until evenly combined, about 1 minute. Add remaining ingredients and process until evenly blended, about 1 more minute. Taste and adjust seasoning, as desired.
For the lasagna: Heat oven to 375 degrees F and arrange rack in upper third.
Meanwhile, alternatively layer a scant 1/4 cup pesto and 1 sheet of fresh lasagna noodles in an 8 by 8-inch baking dish, trimming noodles, as needed, to fit. There should be about 10 to 12 layers. Top lasagna with cheese and bake until bubbly around edges and cheese is melted, about 20 to 25 minutes. Let sit at least 20 minutes before serving.