Preheat oven to 400 degrees.
Cut acorn squash in half between stem and bottom. Clean out all seeds.
Cut butternut squash in half between stem and bottom. then cut each piece in half the other direction, through the stem and bottom of squash, Clean out all seeds.
Lay cut side down on greased cookie sheet and bake for 30 minutes. Remove from oven and flip each piece over and check with fork, the squash should be very tender. Remove pieces onto cooling rack as they are done, continuing to cook other pieces as needed. Allow to cool enough to handle.
Scoop out all squash into a large mixing bowl. Mash together with large spoon or potato masher.
Turn oven temperature to 350 degrees.
Mix in chicken broth, eggs, salt and pepper.
Heat butter in a large skillet over medium/high heat. Add onions. Stir and cook until tender.
Turn off heat. Add dried Stove Top mixing well.
Add about ¾ of the Stove Top/butter mixture into the squash. Mix together.
Pour into lightly greased 9x13 pan.
Sprinkle remaining Stove Top mixture over top. Bake for 35 minutes.