Mash garlic in a medium bowl using a fork. Whisk in rosemary, 2 tablespoons olive oil, 1 tablespoon lemon juice, and 1 ½ teaspoons salt. Add chicken to marinade, turning to evenly coat. Cover and refrigerate at least 30 minutes or up to 24 hours.

Meanwhile, bring beans, 2 cups water, and ½ teaspoon salt to a simmer in a medium saucepan over medium-high. Remove from heat; let beans rest in cooking liquid for 10 minutes. Drain beans, reserving 2 tablespoons cooking liquid; discard remaining cooking liquid. Do not wipe saucepan clean. Reserve ⅓ cup beans; return remaining beans to saucepan, and set aside.

Place reserved ⅓ cup beans and reserved 2 tablespoons cooking liquid in a blender. Secure lid on blender, and remove center piece to allow steam to escape. Place a clean towel over opening; process until a slightly loose puree develops, about 15 seconds. Add ¼ cup olive oil, ¾ teaspoon salt, and remaining 1 tablespoon lemon juice; process until smooth, about 30 seconds. Stir pureed beans into saucepan with whole beans. Cover and keep warm.

Preheat oven to 425°F. Pat grape leaves dry. Arrange 4 overlapping leaves per chicken breast on a clean work surface. Place a chicken breast, horizontally, on each set of leaves. Sprinkle chicken breasts evenly with remaining ½ teaspoon salt. Fold in sides of grape leaves, and roll up to form a packet; set aside. Repeat wrapping process with remaining chicken and remaining grape leaves.

Heat remaining 1 tablespoon olive oil in a large ovenproof skillet over medium-high. Add grape leaf parcels, seam sides up; cook, turning once halfway through cooking time, until seared on both sides, about 2 minutes per side. Arrange grapes in skillet around parcels.

Transfer skillet with chicken to oven. Bake until a thermometer inserted into thickest portion of chicken registers 160°F, 12 to 15 minutes. Transfer grape leaf parcels to a platter, and let rest.

Return skillet to stovetop, and heat over medium; cook grapes and juices, stirring often, until grapes are caramelized, about 2 minutes. Add vinegar, and increase heat to high. Cook, stirring often, until syrupy but not entirely dry, about 3 minutes. Add any juices from resting chicken to skillet; cook until 2 to 3 tablespoons of liquid remain, about 30 seconds, stirring often. Add ¼ cup butter, and swirl skillet to melt and emulsify, about 1 minute. Remove from heat.

Return beans in saucepan to a simmer over medium. Add kale; cook, stirring constantly, until just wilted, about 1 minute. Stir in remaining 2 tablespoons butter until melted, about 1 minute. Season with additional salt to taste.

Serve chicken with beans and with sauce spooned over top, and garnish with herbs.