Roasted Cornish Game Hens

Squeeze 1 lemon to yield 2 tablespoons juice; discard seeds and squeezed rind. Cut 1 lemon into 6 wedges. Cut remaining 3 lemons in half crosswise. Set aside.

Place lemon juice, chopped rosemary, chopped thyme, oil, salt, pepper, paprika, and 10 garlic cloves in a food processor; process until garlic is finely chopped and mixture is blended, stopping to scrape down sides as needed, about 2 minutes. Rub mixture evenly over Cornish hens and inside the cavities. Fill each cavity with 3 lemon wedges and 5 garlic cloves. Truss each hen with kitchen twine by tying together the legs and tightly wrapping twine around each hen to securely hold wings to breasts. Arrange rosemary sprigs and thyme sprigs in an even layer in a large roasting pan. Place hens and lemon halves on top of herb sprigs. Let rest at room temperature, uncovered, for 1 hour

While hens rest, preheat oven to 425°F. Cover roasting pan with aluminum foil. Roast for 25 minutes. Remove hens from oven. Remove and discard foil; add broth to roasting pan. Continue roasting hens uncovered until skin is deep golden brown and a thermometer inserted into thickest portion of meat registers 165°F, 25 to 35 minutes longer. Remove from oven; let hens rest in pan at room temperature 5 minutes. Transfer hens and lemon halves to a cutting board; let rest 5 minutes.

Meanwhile, pour remaining mixture in roasting pan through a fine mesh strainer into a small saucepan; discard solids. Bring juices in saucepan to a low boil over medium. Remove from heat, and whisk in butter, 1 piece at a time, until well combined. Season to taste with salt.

Carefully cut each hen in half lengthwise. Serve with roasted lemon halves and pan sauce.