In a small bowl, mix together the garlic powder, Italian seasoning, onion powder, paprika, 1 teaspoon of the salt, and ½ teaspoon of the pepper. Pat the chicken dry with a paper towel, then season all sides with the spice mixture, rubbing it in to coat.

In a large cast-iron skillet, heat the oil over medium heat. Add the chicken thighs, skin-side down, and cook until golden brown, about 4 minutes. Remove to a plate.

Arrange the carrots and potatoes in a single layer in a 6-quart slow cooker. Scatter the garlic, thyme, and shallots over the top. Season with the remaining 2 teaspoons salt and ½ teaspoon pepper, then pour the chicken broth over everything.

Arrange the chicken, skin-side up, in a single layer on top of the vegetables in the slow cooker. Scatter the cubed butter over the top. Cover and cook on low heat for 4 to 6 hours, or on high heat for 2 ½ to 3 hours, until the internal temperature of the chicken is 165°F and the potatoes and carrots are tender.

If you would like a slightly thicker sauce, remove the chicken thighs to a plate. In a small bowl, whisk together the cornstarch and 1 tablespoon water. Add the cornstarch slurry to the slow cooker and stir until incorporated. Add the chicken back to the slow cooker, cover, and cook on high for 5 to 10 minutes, until the sauce is thickened.

Serve the chicken on top of the vegetables. Spoon over some liquid from the slow cooker and sprinkle with parsley, if you like.