Place the chicken, onion, celery, carrots, garlic, oregano, rosemary, bay leaves, and chicken stock in a slow cooker. Add a pinch of salt and pepper, then cover with lid and cook on high for 4 hours.
In the meantime, preheat the oven to 350 F. Separate the biscuits from each other and slice into quarters, pressing down slightly to flatten. Bake the quarters for 6-7 minutes, or until the biscuits are risen but still doughy. Remove from the oven and set aside.
Remove the chicken from the slow cooker and shred using two forks. Return shredded chicken to the slow cooker.
Whisk the cornstarch into the water and pour slurry into the slow cooker. Add the evaporated milk and stir to combine.
Add the par-baked biscuits and dunk into the liquid. Cook for another hour on high, until the liquid is thickened.
With the slow cooker still on, stir in the spinach to wilt. Season to taste with salt and pepper and remove the bay leaves.