Pat the chicken pieces dry with paper towels, then season generously with salt and pepper.
Heat the large pot over medium heat and melt the butter until it’s sizzling and begins to foam.
Add the chicken pieces to the pot, skin-side down if skin is on, and brown them on all sides for about 8-10 minutes, until golden brown. Turn them occasionally to ensure even coloring.
Remove the browned chicken and set aside on a plate. In the same pot, add the chopped onions and sauté for 3-4 minutes until they’re soft and translucent, and smell sweet.
Add the minced garlic and cook for another 30 seconds until fragrant, stirring constantly to prevent burning.
Sprinkle the flour over the onions and garlic, stirring constantly to create a roux, and cook for 2 minutes to eliminate the raw flour taste.
Gradually pour in the chicken broth while whisking constantly to prevent lumps, then add the milk or cream, stirring until the sauce begins to thicken and becomes smooth.
Stir in the dried thyme and return the browned chicken to the pot, nestling it into the sauce. Bring the mixture to a gentle simmer, cover, and cook on low heat for about 30 minutes until the chicken is tender and cooked through.
Uncover the pot and increase heat slightly to thicken the sauce, about 5 minutes, until it reaches a velvety consistency, tasting and adjusting seasoning as needed.
Gently stir the chicken to coat with the rich sauce, then turn off the heat and let it rest for a minute.
Serve the chicken fricassee hot, spooning the creamy sauce over the tender pieces, with your favorite sides.