Preheat your oven to 400°F.

Prepare the carrots and potatoes. Peel the carrots. You can peel the potatoes if you'd like, but if you don't mind the skins, then you can leave them on. Chop the carrots and potatoes into 1 to 1.5-inch thick chunks. You want them to be easily biteable once cooked but not so small that they turn to mush while cooking in the braising liquid. 

Prepare the chicken thighs. Lay them out on a clean plate or baking tray, pat dry with a paper towel, and season both sides with salt and pepper to your liking. 

Sear the chicken thighs. Heat 1 tablespoon of oil in a large braising dish over medium-high heat. Once hot, place the chicken thighs in the pan, skin side down, and sear for about 5 minutes, until golden brown. Remove them from the pan and set aside. 

Saute the garlic and onion. Reduce the heat, add the minced garlic and diced onion, and cook for about 2-3 minutes over medium heat (don't let the garlic burn).

Deglaze the pot with the white wine. Let simmer for about 1 minute.

Add the carrots, potatoes, ½ teaspoon kosher salt, ¼ teaspoon ground pepper, sage, thyme, and rosemary, and give it a good stir to combine with the garlic and onions.

Pour the chicken stock and lemon juice into the pan.

Place the thighs back in the pan, skin side up. Nestle them down into the carrots and potatoes as much as possible.

Cover your braising dish with a tight-fitting lid and bake the chicken thighs, carrots, and potatoes for 40 minutes or until the thighs have reached an internal temperature of at least 175°F.  

Once cooked through, remove the lid and broil the tops of the chicken thighs under high heat for about 5 minutes to crisp the skins. Keep an eye on them to make sure they don't burn!

Make the gravy. First, remove the chicken thighs, potatoes, and carrots from the dish using a slotted spoon. Then, carefully pour the braising liquid into a large liquid measuring cup. Reserve 2 cups of the braising liquid and discard the rest. You should easily have 2 cups of liquid in your pan, but if you're short, you can make up the difference with water or chicken broth.   

Add the butter to your (now empty) braising dish and melt over medium-low heat.

Add the flour and whisk or stir the flour and butter into a smooth paste. Cook for 1 minute, whisking constantly.   

Pour the pan liquids back into the dish with the butter and flour and stir until smooth. Continue stirring until the mixture thickens into gravy.

Serve your braised chicken thighs, carrots, and potatoes with gravy drizzled over top.