Season chicken thighs generously with salt and pepper on both sides. Brown the chicken in a skillet with a tablespoon of olive oil before transferring to the slow cooker.
Sauté the diced onion in the remaining tablespoon of olive oil until translucent (about 3-4 minutes). Add minced garlic and cook for 30 seconds until fragrant.
Place the browned chicken in your slow cooker. Add the onion-garlic mixture, lemon zest, lemon juice, thyme, rosemary, and 1 tablespoon of parsley. Pour in the chicken broth and stir gently to combine.
Cover and cook on low for 6-7 hours or high for 3-4 hours, until the chicken easily shreds with a fork.
About 30 minutes before serving, whisk together heavy cream and cornstarch mixture. Gently stir this into the slow cooker, being careful not to break apart the chicken. Cover and cook on high for an additional 20-30 minutes until the sauce thickens.
Just before serving, taste and adjust seasonings if needed. Gently stir in the remaining tablespoon of fresh parsley.