Melt butter in a large deep skillet over medium heat.
Add diced onions and cook, stirring occasionally, until translucent and slightly browned, about 3-5 minutes.
Stir in flour and season with salt and pepper, combining thoroughly.
Pour in chicken stock, stirring to blend with the flour mixture.
Slowly add half-and-half while stirring constantly until smooth.
Increase heat and cook, stirring, until the sauce thickens, about 1-2 minutes.
Add dried tarragon, peas, and cooked chicken, then warm through for a few minutes.
Adjust seasoning with salt and pepper as needed.
Serve the creamed chicken gravy over warm biscuits.