Adjust oven rack to middle position and heat oven to 400 degrees. Set wire rack in rimmed baking sheet. Combine 3/4 teaspoon salt, 1/4 teaspoon pepper, and paprika in bowl.

Pat hens dry with paper towels. Sprinkle evenly all over with salt mixture and rub in mixture with your hands to coat evenly. Tuck wingtips behind backs and lay hens breast side down on prepared wire rack. Roast hens until backs are golden brown, about 25 minutes.

Meanwhile, bring 1/4 cup honey and 1 tablespoon vinegar to simmer in small saucepan over medium-high heat. Whisk together 2 teaspoons water and 1/2 teaspoon cornstarch in bowl, then whisk into saucepan. Continue to simmer until thickened, 1 to 2 minutes. Remove from heat and cover to keep warm.

Remove hens from oven and brush backs with one-third of glaze. Flip hens breast side up and brush with half of remaining glaze. Continue to roast for 15 minutes.

Remove hens from oven and increase oven temperature to 450 degrees. Pour remaining 1/2 cup water and broth into baking sheet. Brush hens with remaining glaze and continue to roast until glaze is spotty brown and breasts register 160 degrees and thighs register 175 degrees, 5 to 10 minutes. Transfer hens to serving platter and let rest, uncovered, for 10 minutes.

Pour liquid from baking sheet into now-empty saucepan and let settle for 5 minutes. Using large spoon, skim excess fat from surface of liquid. Stir in thyme and remaining 1 tablespoon honey, bring to simmer, and cook until sauce is reduced to 1/2 cup, 2 to 6 minutes.

Whisk together remaining 2 teaspoons vinegar and remaining 1/2 teaspoon cornstarch in bowl, then whisk into saucepan. Continue to simmer sauce until thickened, 1 to 2 minutes. Stir in any accumulated juices and simmer for 30 seconds. Off heat, whisk in butter and season with salt and pepper to taste. Serve hens with sauce.