In a large skillet with a cover, over medium heat, saute the onion in 2 tablespoons olive oil until translucent.
Add the mushrooms and continue to saute for another 5 minutes, stirring occasionally.
Stir the garlic into the onions and mushrooms to coat with the oil. Set the heat to medium low.
Pile the spinach on top of the mushroom mixture, cover, and let steam until the spinach is well wilted. Stir mixture to coat the spinach.
Move the spinach mixture to a colander and press with the back of a spoon to remove most of the liquid. Allow to cool sufficiently that it will not cook the eggs. (This is a good time to start assembling the bottom layer of phyllo.)
In a medium bowl, whisk together the eggs, salt and pepper. Fold the crumbled feta and drained spinach mixture into the eggs.
Preheat the oven to 400F while you work with the phyllo and filling. Using a brush and the remaining 1/4 cup of olive oil, assemble the spanakopita.
For the bottom layer, oil a 9"x13" baking pan. Lay a sheet of phyllo on the pan and brush lightly with olive oil. Repeat with 1/3 of the phyllo sheets (6-8 sheets). Spread with 1/2 the filling.
Repeat with the next 1/3 of the sheets of phyllo, lightly spreading oil on each. Cover with the other half of the filling.
Top with the remaining sheets of phyllo, oiling each, making sure the top layer is thoroughly coated with oil. Poke any dry edges sticking up down into oil and filling.
Bake 40 minutes until golden on top. Allow to sit ten minutes or more before serving.