Preheat your oven to 375°F (190°C). Have a 9x13-inch baking dish or large cast-iron skillet ready.
Heat olive oil in a large skillet over medium-high heat. Season chicken pieces with salt and pepper, then add to the hot skillet. Cook until golden brown on all sides, about 5-6 minutes. The chicken doesn't need to be fully cooked through. Transfer to a plate and set aside.
In the same skillet, add onions, carrots, and celery. Cook until vegetables begin to soften, about 5-7 minutes. Add garlic, thyme, and rosemary and cook for another 30 seconds until fragrant.
Sprinkle flour over the vegetables and stir for 1-2 minutes. Gradually whisk in chicken broth, stirring constantly to prevent lumps. Bring to a simmer until slightly thickened, then stir in heavy cream. Return the chicken to the skillet along with frozen peas and fresh parsley. Season with salt and pepper to taste.
In a large bowl, whisk together flour, baking powder, sugar, garlic powder, salt, and cayenne pepper. Add grated cheddar cheese and toss to coat. Using your fingers or a pastry cutter, work the cold butter into the flour mixture until it resembles coarse crumbs. Stir in buttermilk until just combined - do not overmix.
Transfer the chicken mixture to your baking dish if not using an oven-safe skillet. Drop spoonfuls of the biscuit dough on top, leaving some space between them for expansion.
Combine melted butter with dried parsley and garlic salt. Brush this mixture over the biscuit tops.
Bake for 25-30 minutes, or until the filling is bubbling and the biscuits are golden brown and cooked through. Allow to cool for 5-10 minutes before serving.