Place the onions in a bowl and cover them with boiling water. Allow them to sit for 5 minutes; drain. Slice off the tops and peel.
Preheat oven to 400 F and line a baking pan with a silicone baking mat or parchment paper. Remove the tops of the radishes (save, if they’re fresh) and trim off the tails. Slice any larger radishes in half, keep the smaller ones whole, and place them all in the baking pan. Add the prepared pearl onions. Spray lightly (1 second) with olive oil and sprinkle with salt and freshly ground black pepper. (The tiny amount of oil prevents the radishes from drying out; you can skip it, but your results might not be as good.)
Peel off the very outermost layers of the garlic. Use a sharp knife to cut about 1/2-inch off the top of the bulb, exposing the tops of the cloves. Wrap in aluminum foil, and place it in a corner of the baking pan. Put the pan in the oven and roast, stirring every 10 minutes, until a fork easily pierces a radish, about 30 minutes. Remove the garlic and set aside to cool. Toss radishes and onions with 1 teaspoon of vinegar and set aside until quinoa is done.
While the vegetables are roasting, rinse the quinoa well. Place it in a medium-sized sauce pan and add the vegetable broth, oregano, and freshly ground pepper to taste. If you like, chop a handful or two of the radish greens (well washed) and add them to the pan. Bring to a boil, cover tightly, and reduce to a simmer. Cook until all water is absorbed, about 20 minutes.
When both quinoa and vegetables are done, add the vegetables to the quinoa. Squeeze as many as you like of the cloves from the garlic and mash them lightly. Add the garlic to the quinoa along with salt, pepper, and additional vinegar to taste. Serve warm, garnished with chopped parsley.