To prepare filling, place spinach in a large skillet or Dutch oven. Place over medium heat; cook until spinach wilts. Place the spinach mixture in a colander, pressing until barely moist. Combine the spinach and cheeses in a bowl; set aside.
Heat 2 teaspoons olive oil in a nonstick skillet over medium-high heat. Add the green onions; sauté for 2 minutes or until soft. Stir the green onions and the next 5 ingredients (green onions through 2 egg whites) into spinach mixture.
Combine 1 tablespoon olive oil, 1/4 teaspoon salt, and 1 egg white in a small bowl, stirring with a whisk. Working with 1 phyllo sheet at a time, cut each sheet lengthwise into 4 (3 1/2-inch-wide) strips; lightly brush phyllo sheet with egg mixture (cover the remaining phyllo dough to keep it from drying). Spoon about 1 tablespoon spinach mixture onto one end of each strip. Fold one corner of the opposite end over mixture, forming a triangle; keep folding back and forth into a triangle to the end of strip.
Place triangles, seam sides down, on a baking sheet. Bake at 350 degrees F for 20 minutes or until golden.