Here are a few things that may really help:
Do not completely melt the butter. Allow it to just soften to the point where you can mash it with a fork.
Add butter to the mixer first. Let the mixer whip the butter til it gets slightly creamy then add other wet ingredients.
Add eggs 1 at a time.
For the eggs-the omega 3 eggs seem to be a bit fuller I dont know. And this could give the recipe more moisture and turn the cookies into a cake like texture. Try just regular eggs.
It's ok to use the whisk like attachment on the mixer when mixing the wet ingredients. Maybe switching to the cookie attachment or the dough hook once you start adding the dry ingredients to the mixture.
If you dont have the dough hook or cookie attachment. Just use a fork and start to fold the dry ingredients into the mixer and keep folding and lightly stirring with the fork.
Also check and make sure you are using all purpose flour for your cookie recipe. The tollhouse recipe calls out baking soda instead of baking powder. Also something to keep in mind.