Preheat the oven to 350 degrees F. Grease a 9-inch loaf pan and set aside.
Chop the vegetables into 1-inch pieces. Add them to a food processor fitted with a steel blade, and pulse until finely chopped, about 10 1-second pulses.
Heat the oil in a skillet and add the vegetables and garlic, until the vegetables have softened, about 2 – 3 minutes. Season with thyme, salt and pepper. Remove from heat and let cool for 5 minutes.
Add the turkey, vegetables, quinoa, egg and a bit more salt and pepper to a large mixing bowl. Stir until fully combined.
Transfer the meat mixture to the loaf pan, smoothing the top over with a wooden spoon. Smother in barbecue sauce and bake for 45 minutes.