1To make sushi rice, place rice in fine-mesh colander and rinse well to remove excess starch; drain. Transfer to a 2 1/2- to 3-quart heavy saucepan. Add water. Cover with tight fitting lid and bring to boil. Reduce heat to low or medium-low. Very gently simmer, covered, about 20 minutes or until water is absorbed. Remove from heat. Let stand, covered, for 15 minutes.
2Transfer rice to a large baking dish or bowl. Slightly cool. Sprinkle with rice vinegar; toss until combined. Cool to room temperature. Cover with damp towel to prevent rice from drying out.
3Meanwhile, for spinach-egg filling, squeeze excess moisture from spinach. Finely chop spinach. Combine spinach, eggs, and salt in small bowl. Heat oil in medium skillet over medium heat. Add spinach-egg mixture. Cook, stirring occasionally, until cooked through but still glossy. Remove from heat. Cool to room temperature.
4To assemble sushi rolls: For each roll, place seaweed sheet, shiny side down, on bamboo matt. Using wet hands, spread a scant 1 1/4 cups sushi rice evenly on seaweed sheet to within 3/4 inch of edge nearest you and opposite side. Place 1 1/2 or 2 slices of ham across the center of the rice. Spoon about 3 tablespoons of spinach-egg mixture in a strip across the ham.
5Use bamboo matt to lift and tightly roll sushi, jelly-roll style. Shape roll by lightly pressing roll together with damp hands. If desired, tightly wrap sushi rolls in plastic wrap and refrigerate for up to 2 hours. To serve, using a wet knife, slice each roll into 6 to 8 pieces. Makes 24-32 pieces