Preheat oven to 425°F. Spray a 2 ½ - 3-quart casserole dish with cooking spray and set aside.
In a separate bowl, whisk together chicken broth and half-and-half. Set aside.
Melt butter in a large skillet over medium-high heat. Add onion, carrot, and celery; sauté for 10 minutes. Add flour and continue cooking and stirring for 1 more minute. Reduce heat to medium and gradually stir in the chicken broth mixture.
Continue cooking over medium heat, stirring regularly, until thick and bubbly (about 5-6 minutes). Make sure that the mixture doesn’t boil. Stir in the salt and pepper. Add chicken and frozen peas.
Transfer the mixture to the prepared baking dish. Cover with foil and bake for about 10 minutes while you prepare the biscuit dough.
PREPARE BISCUITS:
Use a fork to stir together the Bisquick mix, buttermilk, cheese and parsley until a soft dough forms. Start with ⅔ cup of buttermilk, and gradually add more (if needed) to bring the dough together. It shouldn't be too wet, but you don't want any dry pockets of flour.
Remove the chicken mixture from the oven, take off the cover, and give the filling a stir. Use a scoop to drop about ¼-cup of the biscuit dough (or even slightly less) at a time onto the hot chicken mixture. You should have about 8 biscuits on top of the dish. You can use a larger scoop to drop 6 biscuits on top, but these larger biscuits will take longer to bake through.
Return dish to the oven and bake, uncovered, for about 12 minutes, or until golden brown and a toothpick inserted in a biscuit comes out clean. If the biscuits start to get too dark on top before they're cooked through, just tent loosely with aluminum foil and continue baking.
Stir together melted butter and garlic powder; brush over warm biscuits and serve.
Video
Notes
If you have a large (about 3-quart)oven-proof skillet or braiser, you can prepare the filling and bake the casserole all in the same dish. One less item to wash at the end! I used this 12-inch cast iron skillet in these photos.
For a thicker filling with biscuits that are closer together, use a smaller, deeper 2-quart baking dish.
Do not thaw the frozen peas before adding them to the filling.
Use a smaller scoop (about ¼-cup or less) to make smaller biscuits, which will cook through easier than larger biscuits.
Make sure that the biscuits are cooked all of the way through before pulling the casserole out of the oven. They should be golden brown on the outside and a toothpick inserted in the center should come out clean.
If the biscuits start to get too dark before they're completely cooked through, tent the dish with foil and continue baking.