Brush bottom of the slow cooker with butter.
Evenly sprinkle the shallots into the pot.
Season chicken pieces with salt and ground white pepper.
Arrange chicken on top of the shallots.
Top with fresh sprigs of tarragon.
Pour in wine and chicken stock and cook on low for 4 hours.
Strain cooking stock into a saucepan.
Set over medium heat and allow to reduce.
Whisk in heavy cream, cold butter nuggets, and chopped tarragon leaves.
Season with salt and pepper if needed.