Step 1

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.

Step 2

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.

Step 3

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.

Step 4

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.

Step 5

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.

Step 6

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.

Step 7

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.