Preheat oven to 375°F. Heat 3 tablespoons extra virgin olive oil (evoo) in a large skillet over medium-high heat. Add onion and sauté 4 minutes, or until slightly softened.
Add mushrooms and garlic; sauté 5 to 7 minutes more, or until tender
Stir in spinach and cook 2 minutes; cool for 10 to 15 minutes.
Working with one turkey breast at a time, carefully slice horizontally through the middle, without cutting all the way through, to make a large pocket in the center.
In a large bowl, combine mushroom and spinach mixture with egg, matzoh meal, parsley, salt, and pepper flakes; stir to combine.
Divide mixture evenly between each turkey breast and stuff to fill the pocket.
Heat remaining 3 tablespoons evoo in a large dutch oven or heavy bottomed saucepan over medium-high heat. Sear turkey breasts for 3 to 5 minutes per side until lightly browned.
Carefully add broth; cover and transfer to preheated oven. Cook 45 minutes or until internal temperature reaches 165°F.
Let rest 10 minutes before cutting each breast into 8 slices.