Heat 1/2 cup of extra virgin olive oil in a small saucepan over medium-high heat until very hot.
In a heatproof bowl, mash 1 1/2 teaspoons of ground cumin, 1 1/2 teaspoons of kosher salt, 1/2 teaspoon of oregano, and 2 tablespoons of minced garlic together into a paste.
Whisk the hot oil into the paste and allow the mixture to cool slightly.
Add 3 tablespoons of lime juice and 3 tablespoons of orange juice to the mixture, and stir well.
Place the cut chicken in a large sealable bag, pour the marinade over the chicken, and shake to ensure an even coating.
Refrigerate the marinated chicken for at least 4 hours, or up to overnight.
Preheat the oven to 375 degrees F (190 degrees C) and arrange the marinated chicken in a roasting pan.
Bake the chicken in the preheated oven for about 1 hour, or until no longer pink at the bone and the juices run clear.
Check the chicken's temperature with an instant-read thermometer; it should read 180 degrees F (82 degrees C) when inserted into the thickest part of the thigh near the bone.