Place the spinach in a large dish towel or double layer of paper towels and squeeze to remove as much excess moisture as possible. Set aside.

Melt 1 tablespoon of butter in a large skillet over medium heat. Add the onion, scallions, and garlic. Cook, stirring occasionally, until the onions are softened, 8 to 10 minutes. Transfer the mixture to a large bowl and let cool for 10 minutes.

Add the eggs, feta, cottage cheese, parsley, dill, salt, pepper and drained spinach to the onion mixture. Stir until well combined.

Preheat the oven to 375°. Melt the remaining 9 tablespoons butter in a small microwavable bowl in 15 second intervals in the microwave. Brush a 9-by-13-inch baking dish generously with butter. Place two sheets of phyllo dough in the bottom of the dish, layered on top of each other. Brush the top with butter. Repeat the process 3 more times, for a total of 8 phyllo sheets, brushing with butter every other layer. Spread the spinach mixture evenly over the crust. Top with 2 phyllo sheets and brush the top with butter. Repeat with the remaining 6 phyllo sheets, brushing with butter every other layer. Drizzle any remaining butter evenly over top of the spanakopita.

Score the top crust of phyllo sheets into 15 pieces using a paring knife. (This will make cutting after baking easier.) Bake the spanakopita until golden brown and flaky, 45 to 55 minutes. Serve hot.