Preheat the oven to 375 degrees F.

Combine in a food processor the achiote paste, olive oil, cumin, coriander, oregano, and 1 tablespoon garlic. Make sure to puree all these ingredients until it becomes a paste. Rub the marinade inside the Cornish hen cavities, underneath the skin, as well as outside. Allow the hens to marinade overnight, refrigerated.

Next day, heat up a large saute pan. Add the chorizo and cook until crispy, about 5 minutes. Add the onion and remaining 4 tablespoons garlic and cook for another 2 minutes. Add the mustard greens and deglaze with the chicken stock. Cook until greens have wilted, about 2 minutes, and then add the potato, green olives, and season, to taste, with salt and pepper. Once the stuffing has cooled, distribute it equally into the hens and place them on a sheet with a rack. Place in the oven for 1 hour.