Slow Cooker Chicken With Garlic and Potatoes

Haul out your slow cooker—preferably a 5-quart (4.7-liter) baby—and place the carrots or celery in a single layer in it.
Remove the skin as well as any excess fat from the chicken. In a small bowl, stir together the rosemary, sweet smoked Spanish paprika, 1 1/2 teaspoons salt, and 1 teaspoon pepper. Rub the mixture all over the chicken.
In a large skillet over medium heat, warm 3 tablespoons oil. When the oil is hot, add the garlic and sauté until golden brown, 1 1/2 to 2 minutes. Use a slotted spoon to place the garlic in a bowl, reserving the oil in the skillet.
Add half of the chicken to the reserved oil and cook until deep golden brown, 3 to 5 minutes per side. Place the seared chicken in the slow cooker, leaving the drippings in the skillet. Repeat with the remaining chicken.
Add the broth and garlic to the reserved drippings in the skillet. Cook, stirring and scraping the skillet, for 1 minute. Pour the mixture over the chicken in the slow cooker. Cover and cook on HIGH for 2 hours.
In a medium bowl, toss the potatoes with 1 teaspoon oil, 1 teaspoon salt, and 1⁄4 teaspoon pepper. At the end of the 2 hours, add the potatoes to the slow cooker. Cover and cook until the potatoes are cooked through and the chicken is very tender, about 2 hours more.
Pile the chicken and potatoes onto a platter. Strain the juices from the slow cooker into a bowl. Skim the fat from the juices, if desired, and pass on the side with the chicken and potatoes.