Start CookingCHICKEN FILLING
Place the butter for the biscuit dough in the freezer so it gets very cold while you make the filling.
Preheat the oven to 400°F.
In a medium skillet over medium heat, melt the butter, then toss in the carrots, onion, and celery. Cook for 7 to 8 minutes, stirring occasionally with a wooden spoon, until softened with some browning and caramelization.
Stir in the garlic, sage, thyme, and rosemary and cook for 1 minute until fragrant.
Sprinkle the flour over the vegetables, stir to coat, and cook for 1 minute.
Slowly pour in the chicken broth while whisking with a hand whisk to avoid lumps, then pour in the half and half. Simmer for 2 to 3 minutes until the sauce thickens slightly.
Season with the salt, black pepper, smoked paprika, red pepper flakes, mustard, turmeric, and nutmeg, then taste and adjust.
Fold in the shredded chicken and peas and simmer for 3 to 4 minutes until heated through, then remove from the heat.
Divide the filling between two 5.5-inch skillets, or spread it into one large baking dish, and set on a baking sheet.
BISCUIT DOUGH
In a large bowl, combine the flour, sugar, baking powder, salt, garlic powder, oregano, parsley, and cayenne, then whisk with a hand whisk until evenly mixed.
Using the large holes of a box grater, grate the very cold butter directly into the flour mixture, then toss with a rubber spatula until the butter shreds are coated.
Pour in the buttermilk and fold with the rubber spatula until mostly combined.
Sprinkle in the cheddar and fold just until a shaggy dough forms.
GARLIC & HERB BUTTER
In a small bowl, stir together the melted butter, parsley, garlic, parmesan, black pepper, and salt until combined.
ASSEMBLE & BAKE
Using a cookie scoop or ice cream scoop, drop 3 to 4 rounds of dough over the filling in each skillet. If using a large baking dish, scoop on enough rounds to almost cover the entire top.
Bake for 20 to 25 minutes or until the biscuits are golden and fully cooked through.
Optional, if needed: Switch the oven to broil and broil for 2 to 3 minutes until the tops are deep golden.
Brush the garlic herb butter all over the hot biscuits with a pastry brush, let cool for 5 minutes, then enjoy!