Heat the oven to 400 degrees. Coat a large rimmed baking sheet with non-stick cooking spray. Place the spaghetti squash, cut-side down, on the baking sheet. Toss the chicken breasts, bell pepper and zucchini in a large bowl with oil; sprinkle with salt and pepper. Place on the baking sheet around the spaghetti squash.
Bake for 30 to 40 minutes or until the spaghetti squash and vegetables are tender and the chicken is no longer pink in the center. With a fork, shred the chicken into large pieces; place in a medium bowl. Add the roasted vegetables, cottage cheese and pesto.
Using a fork, shred half of the spaghetti squash into spaghetti-like strands; place in a bowl and toss with the chicken, vegetables, cottage cheese and pesto. Spoon into the center of the spaghetti squash; place on clean large rimmed baking sheet. Top with the mozzarella cheese. Bake for 20 to 25 minutes or until hot and the cheese is melted.