Preheat oven to 350 degrees F. Lightly coat a 12-cup muffin tin with cooking spray.
Heat 1 tablespoon oil in a medium skillet over medium heat. Add onion and 1/8 teaspoon salt; cook, stirring, until starting to brown, about 4 minutes. Remove from heat. Set aside to cool for 5 minutes.
Whisk eggs, spinach, feta, milk, dill, pepper, the remaining 1/8 teaspoon salt and the cooked onions in a large bowl.
Lay phyllo sheets on a clean, dry work surface. (Cover the sheets with a kitchen towel to keep them from drying out while you assemble the cups.) Pour the remaining 2 tablespoons oil in a small bowl. Place a sheet of phyllo on a clean cutting board. Lightly brush with oil. Lay another sheet of phyllo on top and lightly brush with oil. Cut the phyllo into 6 pieces (in half horizontally and in thirds vertically). Place one square in a muffin cup, pressing it down the bottom and sides. Add another square, alternating the position so the sides of the muffin cup are covered. Repeat the process with the remaining squares; then with the remaining phyllo sheets and oil.
Fill each phyllo cup with a scant 1/4 cup of the egg mixture. Bake until the filling is firm to the touch and the phyllo is lightly browned, 25 to 30 minutes.
Equipment: Standard 12-cup muffin tin