Preheat oven to 425°. Wrap two bricks in
aluminum foil.
Boil rum and turbinado sugar for the glaze in
a small saucepan over medium heat until
syrupy, about 10 minutes. Off heat, stir in
lime juice. Transfer glaze to a bowl. When it
cools, stir in mint.
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Combine oil, brown sugar, cumin, garlic
powder, oregano, and salt in a small bowl.
Heat a large grill pan or sauté pan over
medium-high heat. Rub both sides of
prepared hen halves with spice mixture.
Place halves in the pan and sear skin side
down. Top with the bricks. Cook until skin is
richly browned but not burned, about 3
minutes. Remove bricks and flip hens over.
Transfer pan to the oven, and roast hen until
an instant-read thermometer inserted into the
thigh reaches 165°, about 15 minutes.
Let hens rest 5 minutes, then drizzle with
glaze before serving
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