1. Place carrots in a single layer in a 5-qt. slow cooker.
2. Remove skin from chicken, and trim fat. Stir together rosemary, pimentón, 1 1/2 tsp. salt, and 1 tsp. pepper. Rub mixture over chicken.
3. Sauté garlic in 3 Tbsp. hot oil in a large skillet over medium heat 2 minutes or until golden brown. Transfer to a bowl using a slotted spoon; reserve oil in skillet. Cook half of chicken in reserved oil in skillet 3 to 4 minutes on each side or until deep golden brown. Transfer to slow cooker, reserving drippings in skillet. Repeat with remaining chicken.
4. Add broth and garlic to reserved drippings in skillet, and cook 1 minute, stirring to loosen particles from bottom of skillet; pour over chicken in slow cooker. Cover and cook on HIGH 2 hours.
5. Toss potatoes with 1 tsp. oil and remaining 1 tsp. salt and 1/4 tsp. pepper; add to slow cooker. Cover and cook 2 more hours.
6. Transfer chicken and potatoes to a serving platter, and pour juices from slow cooker through a fine wire-mesh strainer into a bowl; skim fat from juices. Serve immediately with chicken and potatoes.
The Art of Browning Browning meats and poultry before simmering in the slow cooker yields major depth of flavor plus a picture-perfect presentation, so don't be tempted to skip it. First, pat the meat dry with paper towels before seasoning. Set a heavy stainless-steel or well-seasoned cast-iron skillet (not nonstick) over medium to medium-high heat for 2 to 3 minutes or until hot enough for the oil to shimmer--the meat should hiss and sizzle as soon as it hits the pan. Be sure not to crowd the pan; doing so drops the temp, causing the meat to steam rather than form a crisp crust. Don't turn the meat until the bottom is well-browned.