Preheat your oven to 425°F.

Thoroughly rub each Cornish hen inside and out with 1 tablespoon of butter per bird.

Season each hen generously with salt, pepper, and a light sprinkle of paprika.

Place one piece of onion and one piece of celery inside each hen's cavity.

Tie the legs of each hen together with kitchen twine to ensure even cooking.

Arrange the hens in a roasting pan, uncovered, and place in the preheated oven.

Roast for approximately 1 hour, basting occasionally with the melted butter to achieve crispy, golden skin.

While the hens are roasting, combine the dried thyme, bay leaf, and Madeira wine in a small bowl and set aside.

Once the hens are cooked through and beautifully browned, remove them from the oven and transfer to a serving platter. Cover loosely with foil to keep warm.

Pour 1/2 cup of the roasting pan drippings into a skillet over medium heat.

Add the finely chopped onion to the skillet and sauté until soft and translucent.

In a separate bowl, mix the cornstarch and sugar into the chicken stock until well combined.

Pour the stock mixture into the skillet with the onions and bring to a boil.

Reduce heat to a simmer and add the reserved wine mixture with thyme and bay leaf.

Simmer for about 5 minutes, stirring occasionally, until the sauce reaches your desired consistency.

Strain the sauce into a gravy boat to remove the herbs and onion pieces, creating a silky, refined Bordelaise sauce.

Serve each Cornish hen on individual plates with the Bordelaise sauce on the side.