Place spinach and water in large microwave-safe bowl. Cover bowl with large dinner plate. Microwave on high power until spinach is wilted and decreased in volume by half, about 5 minutes. Using potholders, remove bowl from microwave and keep covered, 1 minute. Carefully remove plate and transfer spinach to colander set in sink. Using back of rubber spatula, gently press spinach against colander to release excess liquid.
Transfer spinach to cutting board and roughly chop. Transfer spinach to clean kitchen towel and squeeze to remove excess water. Place drained spinach in large bowl. Add remaining filling ingredients and mix. Preheat oven to 375 degrees F and line rimmed baking sheet with parchment paper.
Using pastry brush, lightly brush 14 by 9-inch rectangle in center of parchment with melted butter to cover area same size as phyllo. Lay 1 phyllo sheet on buttered parchment, and brush thoroughly with melted butter. Repeat with 9 more phyllo sheets, brushing each with butter (you should have total of 10 layers of phyllo).
Spread spinach mixture evenly over phyllo, leaving 1/4 inch border on all sides. Cover spinach with 6 more phyllo sheets, brushing each with butter and sprinkling each with about 2 tablespoons Pecorino cheese. Lay 2 more phyllo sheets on top, brushing each with butter (these layers should not be sprinkled with Pecorino).
Working from center outward, use palms of your hands to compress layers and press out any air pockets. Using sharp knife, score pie through the top 3 layers of phyllo into 24 equal pieces. Sprinkle with sesame seeds.
Bake until phyllo is golden and crisp, 20 to 25 minutes. Cool on baking sheet 10 minutes or up to 2 hours. Slide spanakopita, still on parchment, to cutting board. Cut into squares and serve.