Preheat the oven to 425 degrees F.
Coat a 7x11-inch baking dish with nonstick cooking spray.
In a large skillet over medium heat, melt 1/4 cup of the butter.
Add the onions, the carrots, and the celery and cook, while stirring often, until softened, about 6 minutes.
Add 1/4 cup of the flour, the garlic powder, the thyme, and the rosemary to the vegetable mixture and cook, while stirring often, until the vegetables are coated and the mixture is fragrant, about 1 minute.
Gradually add the milk to the vegetable mixture, while whisking constantly, until smooth and slightly thickened, about 3 minutes.
Add the chicken, the peas, 1 teaspoon of the salt, and the pepper to the vegetable mixture and stir to combine.
Transfer the chicken mixture to the prepared baking dish.
Place the baking dish with the chicken mixture on a large-rimmed baking sheet.
Cover the baking dish with aluminum foil and bake until heated through, about 10 minutes.
In a large bowl, add the remaining flour, the baking powder, the sugar, and the remaining salt and whisk until combined and no lumps remain.
Grate the remaining frozen butter on the large holes of a box grater into a bowl.
Add the butter to the flour mixture and stir to evenly coat.
Add the Gruyère cheese and the cheddar cheese to the flour mixture and toss to coat.
Using a rubber spatula, add 3/4 cup of the buttermilk and 2 tablespoons of the chives to the flour mixture, folding to combine, until a shaggy dough forms, about 1 minute. Be careful not to overmix. If the dough seems too dry, add the extra buttermilk, 1 tablespoon at a time, as needed, until the dough comes together.
Transfer the casserole from the oven and remove the foil.
Scoop 1/4-cup-portions of the biscuit dough evenly over the casserole.
Bake, uncovered, until the casserole is bubbly and the biscuits are golden-brown, about 25-30 minutes.
Transfer the casserole from the oven and let it stand for 10 minutes.
Serve garnished with the extra chives.