Rinse the potatoes and place in a pan and cover with cold water. Bring to a boil and cook about 10 minutes just until easily piereced with a fork. Drain and set aside.
Meanwhile add carrots, onion and celery to a deep skillet or dutch oven with bacon grease or olive oil. Cook over medium-high heat, stirring often until vegetables are softened. Remove from pan and set aside with the potatoes.
Preheat the oven to 400°.
Add chicken broth, heavy cream and corn starch to the skillet or dutch oven. Whisk together and add the garlic, thyme, rosemary, salt and pepper. Cook over medium heat, whisking occasionally until thickened.
Remove from heat. Stir in the vegetables and chicken.
Pour into a 9 x 13 inch baking dish and spread evenly.
Make the biscuit dough, and pressing out into a 1/2 inch thick layer on a lightly floured surface. Use a 3 inch biscuit cutter to cut into 12 biscuits.
Layer biscuits over chicken filling.
Bake for 20 - 25 minutes until filling is bubbly and biscuits are lightly browned.
Brush with garlic butter and serve immediately.