Preheat the oven to 375°F (190°C) and arrange a rack in the middle.

Dice the onion, peel and cut carrots and celery into 1/2-inch pieces, and mince the garlic.

Melt 4 tablespoons of the unsalted butter in a large skillet over medium-high heat.

Add onion, carrots, celery, thyme, kosher salt, and black pepper. Cook, stirring occasionally, until vegetables soften and begin to brown, about 5 to 7 minutes.

Sprinkle the flour over the vegetables and add the minced garlic. Stir continuously to coat vegetables evenly and cook until fragrant, about 30 seconds to 1 minute.

Slowly pour in chicken broth and milk while scraping the skillet’s bottom to loosen browned bits. Bring to a boil.

Reduce heat and simmer until sauce thickens to coat the back of a spoon, approximately 4 to 5 minutes.

Stir in the chicken and frozen peas into the thickened sauce. Transfer the mixture evenly into a 9x13-inch baking dish.

Open the can of biscuits and separate them. Arrange in a single layer over the chicken filling in the baking dish.

Bake until biscuits are golden brown and filling bubbles, about 20 to 30 minutes, rotating the dish halfway through.

If biscuits brown too quickly, cover loosely with aluminum foil. Melt the remaining 2 tablespoons of butter and brush over the tops of the biscuits.