Preheat oven to 400 degrees F (204 degrees C)
In a large dutch oven, melt butter over medium heat. Add chopped onion and cook stirring occasionally until onions start to soften. Add garlic and cook for 1 minute while stirring. Add flour and cook for 1 minute while stirring. Whisk in broth and milk until smooth. Cook stirring frequently until mixture starts to thicken (about 5 minutes). Add potatoes, carrots, and celery. Reduce to a simmer, cover and cook for 10-15 minutes or until vegetables are tender.
While the vegetables are cooking start making the biscuits. In a large bowl combine the flour, sugar, baking powder, baking soda, and salt. Cut in the butter using a pastry blender until it resembles coarse crumbs. Or use a box grater and grate the butter then mix into the flour. Stir in the buttermilk (may need to use a little more buttermilk of the buttermilk is really thick).
Place dough on a work surface and knead gently about 10 times just to finish combining the ingredients. Roll or pat into a 10"x6" rectangle. Cut dough into 1" cubes.
When vegetables are tender stir in the chicken or turkey, peas, herbs, salt and pepper. Spoon into a 13x9" baking dish. Top with biscuit pieces.
Bake for 20-25 minutes or until bubbly and golden.