Wash all vegetables under cold water. Dice onion into quarter-inch pieces, slice zucchini thin, peel and chop carrots, cut celery into similar-sized pieces, and mince garlic finely.
Place each chicken breast in a plastic bag and pound with a meat mallet until even thickness throughout. Mix flaky salt, onion powder, garlic powder, and black pepper in a small bowl. Sprinkle seasoning mixture over both sides of each chicken breast and set aside.
In a large soup pot over medium heat, melt the butter. Add zucchini, onion, and garlic. Stir occasionally for 5-7 minutes until zucchini is soft and easily pierced with a fork.
Drizzle olive oil into the pot with the cooked vegetables. Place seasoned chicken breasts in the pot and brown each side for 3-4 minutes until golden.
Transfer cottage cheese, half of the cooked vegetables from the pot, and 1/2 cup chicken broth to a blender. Blend on high until completely smooth with no lumps. Set aside.
Pour remaining chicken broth into the pot with the browned chicken. Add carrots, celery, salt, thyme, parsley, and bay leaves. Stir gently, increase heat to boil, then reduce to a gentle simmer for 15 minutes.
Remove and discard bay leaves with tongs. Transfer chicken to a cutting board with a slotted spoon. Pour blended cottage cheese mixture into the pot and stir well. Add gluten-free pasta.
Shred chicken into bite-sized pieces using two forks and return to the pot. Continue simmering for 10 minutes until pasta is tender. Taste and adjust salt and pepper as needed before serving.