Preheat oven to 425F. In a food processor, add one stick of cold butter. Pulse until roughly chopped. Add flour and salt, and pulse. Slowly add cold water one tablespoon at a time while pulsing until the mixture becomes crumbly.
Use a rubber scraper to take the crust mixture out of the food processor and form into a ball with your hands. Wrap in plastic wrap and refrigerate.
Next, prepare the mushroom filling. Wash and chop mushrooms into slices. Peel and slice onions into rings.
Add butter to a saute pan on medium-high heat and add the onions. Cook until translucent, and then add the mushrooms and red wine. Season with salt and pepper, and cook uncovered until the liquid reduces down, about 10 minutes.
Lay out a sheet of waxed paper and add flour. Take the dough out of the refrigerater, and put it down onto the floured paper. Roll it into a thin circle. Place onto a sheet pan lined with parchment paper.
Pour the cooked mushroom and onion mixture on the center of the crust. Fold the edges over so that you have about an inch and a half border of crust.
Bake for 25 minutes, or until golden brown. Cut like a pizza and serve this elegant Red Wine Portabella Galette as an appetizer or main course!