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1
Crumble feta cheese into a bowl. Add garlic, red pepper flakes, black pepper, lemon zest, oregano, and 3 tablespoons olive oil. Mix and smear into a smooth paste with the back of a spoon. Reserve lemon juice for the sauce.
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2
Preheat the oven to 400 degrees F (200 degrees C).
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3
Season chicken cavity with salt and stuff rosemary and oregano inside. Tie legs together with string, season surface with salt, and tuck wingtips under. Place chicken in a roasting pan.
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4
Tuck fingers under the skin where the breast starts and lift it away from the flesh. Push a small rubber spatula between the skin and flesh and continue loosening the skin all the way down towards the wing. Repeat on the other side. Push a spoonful of the feta filling under the skin. Smooth over the surface of the skin to distribute filling evenly underneath. Repeat until filling is used up.
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5
Rub 2 teaspoons olive oil onto the chicken, smoothing over the skin. Dust the top with cayenne and season with kosher salt.
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6
Roast in the preheated oven until juices run clear and an instant-read thermometer inserted into the thickest part of the thigh registers 155 to 160 degrees F (68 to 71 degrees C), about 1 hour and 10 minutes. Let rest for 15 minutes.
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7
While the chicken is resting, pour off all, some, or none of the fat from the pan, and add lemon juice. Set over medium heat, and use the juice to deglaze the browned bits from the bottom of the pan. Add a splash of broth and adjust seasonings. Slice chicken and spoon sauce on top.
