Add quinoa and vegetable stock to a saucepan and bring to a boil over high heat. Once boiling, reduce heat, cover, and simmer until the liquid is absorbed about 12 minutes. Remove from the heat, fluff with a fork, then cover and let sit for 15 additional minutes.
Preheat oven to 375 degrees F and lightly grease a 9×13-inch baking dish. Arrange the peppers in the dish, cut sides up.
Heat the olive oil in a large, deep saute pan over medium-high. If using fresh spinach, add the spinach in small handfuls, stirring as it wilts down, until you have added all of the leaves. If using frozen spinach, add it in a few larger handfuls, breaking up any clumps of leaves as you go.
To the skillet, add the garlic, basil, salt, and pepper. Let cook 30 seconds, then add the artichoke hearts and cook until warmed through. Remove from the heat. Stir in the quinoa, parsley, 2/3 cup of the cheese, then the Greek yogurt.
Generously stuff the peppers with the quinoa filling. Lightly coat a sheet of foil larger enough to cover the peppers with cooking spray, then cover the dish with foil, spray-side down. Bake for 30 minutes at 375 degrees, covered, then remove foil, sprinkle the remaining 1/3 cup cheese over the top, and continue baking 5-10 additional minutes until peppers are cooked to desired tenderness and the cheese is melted. Serve warm.