Soak the filets in red wine in the refrigerator for a few hours prior to cooking or even overnight.
Preheat the oven to 375ºF.
In a large oven-safe skillet set over high heat, melt 2 tablespoons of the butter. Quickly sear the filets on both sides, about 10-20 seconds per side. Transfer the pan to the oven and cook for 5 minutes for rare, 6-7 minutes for medium, and 7-8 minutes for medium well.
Slice thin to serve.
While the meat cooks, make the sauce. Add the remaining 4 tablespoons butter, pomegranate seeds, blackberries, mushrooms, honey, vinegar, herbs, and salt to a saucepan. Bring to a boil then reduce to a simmer. Cook for 10-15 minutes.
Divide the mixture in half. Blend one half to yield a puree. (A handheld immersion blender works great for this.) Strain through a fine mesh strainer. Spoon the puree on top of the sliced venison.
Top with the reserved unblended sauce.
Notes
If you find cooking with pomegranates daunting, use this simple trick: Score the pomegranate around the center and pry open. Take each half and loosen by pulling and stretching. Turn upside down in your hand over a bowl, and hit the pomegranate with a wooden spoon. The seeds simply fall right out!