Slice the mushrooms very thin, but note they will shrink in the oven. Combine the rest of the ingredients for the marinade, oil through honey. Place mushroom slices in a ziplock bag and pour marinade over top. Seal and let sit at least 2 hours. Preheat oven to 375. Remove mushrooms from bag and place in a single layer on a baking sheet. Place in the oven and cook 25 minutes until slightly browned and almost crisped. Meanwhile prepare the chimichurri: Place all ingredients in a blender or food processor and process until smooth. Serve mushrooms with sauce on top.