Layer the diced yellow onion, sliced carrots, celery, and Yukon Gold potatoes in the bottom of a 6-quart slow cooker.
Heat the olive oil in a large skillet over medium-high heat. Add the chicken pieces and sear for 2 to 3 minutes per side until golden brown (the chicken does not need to be cooked through). Transfer the browned chicken to the slow cooker, placing it on top of the vegetables.
In a medium mixing bowl, whisk together the chicken broth, minced garlic, tomato paste, dried thyme, dried rosemary, salt, and black pepper until well combined.
Pour the broth mixture over the chicken and vegetables in the slow cooker.
Cover and cook on the Low setting for 6 to 8 hours, or on the High setting for 3 to 4 hours, until the chicken is fork-tender and the vegetables are soft.
Thirty minutes before serving, whisk the cornstarch and cold water in a small bowl to create a smooth slurry.
Stir the slurry and the heavy cream into the slow cooker. Cover and continue to cook on High for 20 to 30 minutes until the sauce has thickened and reached a glossy consistency.
Taste and adjust seasoning with additional salt or pepper if desired. Garnish with fresh chopped parsley and serve warm.