Broken Lasagna With Parmesan and All the Peas

Name: Broken Lasagna With Parmesan and All the Peas
Ingredients: Kosher salt; 12 oz. lasagna noodles (not no-boil); 8 oz. snow peas, trimmed (about 3 cups); 1 cup shelled fresh peas (from about 1 lb. pods)or frozen peas, thawed; Zest and juice of 1 lemon; 4 oz. Parmesan, finely grated (about 3 cups), plus shaved for serving; 6 Tbsp. unsalted butter, cut into 6 pieces; 1½ tsp. freshly ground black pepper, plus cracked for serving; 4 oz. sugar snap peas (about 1⅓ cups), strings removed, thinly sliced on a diagonal