Sprinkle the duck pieces with salt and pepper, then dust lightly with flour.
Heat a few tablespoons of olive oil in a large Dutch oven over medium-high heat. Brown the duck pieces on both sides until golden brown. Remove the duck to a plate and pour off most of the fat from the pot. In the same pot, over medium heat, add the garlic, carrots, celery, onions, and red wine. Scrape the pot to dislodge the brown bits stuck to the bottom. Next add the tomatoes and mushrooms, and stir. Place the duck on top of the vegetables and top with the butter and parsley. Reduce the heat to medium-low, cover and cook for 1 hour.
Remove the duck and vegetables to a serving platter. Spoon over the juices and serve warm.
Depending on how fatty the ducks are, it may be nice to render the skin a bit and skip the flouring.