Add the onion, garlic, rice, salt, pepper, and chicken broth to a slow cooker. Stir to combine.
Nestle the chicken breasts into the rice mixture and drizzle with olive oil.
Cover and cook on HIGH for 3-4 hours, until most of the liquid has been soaked up, the rice is tender, and the chicken is cooked through (165°F).
Remove the chicken breasts from the slow cooker and let them rest for 5 minutes. Chop into 1–1 1/2-inch chunks.
While the chicken rests, add all cottage cheese “cream of chicken” ingredients to a blender and blend until completely smooth.
Add the chopped chicken back to the slow cooker along with the broccoli florets and blended cottage cheese mixture. Stir gently to combine.
Sprinkle cheddar cheese on top. Cover and cook for 15–20 minutes, just until the broccoli is tender, the cheese is melted, and everything is heated through.
Turn off the slow cooker and serve.