In a microwave safe bowl, toss the onions, 1/4 cup dried tomatoes, garlic, 1 tbs olive oil, thyme, and red pepper flakes. Microwave in short bursts, stirring as needed, until onion is soft, about 5 minutes.
In your slow cooker, stir the broth, wine, and tapioca together. Add the onion mixture.
Season the chicken thighs with salt and pepper and place in the slow cooker. Cover and cook on low for 4 to 6 hours.
When ready, using two forks, carefully shred the chicken.
Meanwhile, steam the broccoli until tender. Add to the chicken mix along with the cheese and stir to combine. Serve over pasta