Preheat oven to 400°F. Slice the tops off 4 large bell peppers and remove the seeds and ribs. Stand them in a baking dish, trimming the bottoms slightly if they wobble.
In a blender, combine 12 oz whole milk cottage cheese, 2 cloves garlic, ½ tsp chicken or vegetable bouillon base, ½ tsp dried thyme, ½ tsp dried parsley, ¼ tsp onion powder, ¼ tsp salt, and ¼ tsp black pepper. Blend on low just until it comes together. Do not liquefy it. Some curds are fine and the mixture will be very thick.
In a bowl, stir the sauce together with 1½ cups cooked shredded or chopped chicken, 1 15-oz can chickpeas, 1 cup frozen peas and carrots, and ½ cup corn until everything is coated.
Spoon the filling into the peppers, mounding slightly. Bake 30–35 minutes, until the filling is bubbling and set at the edges and a knife slides into the pepper wall with a little resistance. You may have extra filling depending on pepper size. Bake it in a greased ramekin alongside.
For the phyllo: lay one sheet of 2 sheets phyllo dough flat, brush lightly with 1 tbsp melted butter or olive oil spray, lay the second sheet on top, and brush again. Cut the stack into 4 squares. Loosely scrunch each square into a ruffled cloud about the size of a pepper opening. Set on a parchment-lined sheet pan and bake 8–10 minutes until deep golden. Watch closely, they go fast.
Rest the peppers 5 minutes, then set a phyllo cloud on each one right before serving.