Rinse quinoa in a sieve under cold water for at least 2 minutes. Bring a pot of water to a boil. Add salt and cook quinoa for 12-15 minutes. Strain and rinse under cold water. Leave it in the strainer and set aside.
Turn BBQ on to high heat.
Cut peppers in half lengthwise and remove the seeds and core. Leave the tops on. In a large bowl toss with olive oil, salt and pepper.
Place peppers on the grill cut side down. Cook for 8-10 minutes on that side or until the edges are charred. Turn and cook for an additional 4-5 minutes. They are done when just starting to soften, but not limp. Cooking time will vary depending on your BBQ. Remove from grill to a tray and let cool.
In a large saute pan, heat 1 tbsp olive oil over medium-high heat. Add red onion and cook for 2-3 minutes. Add garlic and zucchini. Cook, stirring for 2-3 minutes more. Remove from heat and add cooked quinoa, tomatoes, olives, fresh herbs, and bocconcini cheese. Mix together. Season with salt and pepper to taste.
Preheat oven to 350°F.
In an oiled baking dish, place the peppers together snugly but with enough room to add filling. Fill each pepper generously. At this point peppers can be covered and refrigerated overnight if making ahead.
In preheated oven bake for 15 minutes or until filling is warmed through. Remove from oven, squeeze with lemon juice and sprinkle with crumbled feta cheese. These can be served warm or at room temperature.