Preheat grill to 500 degrees F. Place a brick, wrapped in aluminum foil onto the grates of the grill to heat.
Place the vegetable oil into a 1-quart saucepan and place over high heat. Heat until you see ripples in the in the oil, but do not allow to smoke. Add the fennel, cumin, coriander, mustard seed and paprika. When the seeds begin to pop, remove from the heat and allow to sit for 5 minutes. After 5 minutes, transfer the mixture to the carafe of a blender along with the almonds and salt. Pulse until pureed, stopping to scrape down the sides of the blender, if necessary.
Place the hen breast side down on a cutting board. Using scissors or poultry shears, cut from the neck to the tailbone to remove the backbone. Once you remove the backbone you will be able to see the inside of the bird. Make a small slit in the cartilage at the base of the breastbone to reveal the keel bone. Grab the bird with both hands on the ribs and open up like a book, facing down towards the cutting board. Remove the keel bone. Cut small slits in the skin of the bird behind the legs and tuck the drumsticks into them in order to hold them in place. Place the birds into a baking dish and pour over the puree. Rub the puree onto the birds until thoroughly coated.
Place the birds onto the middle of the grill, skin side down and cover evenly with the brick. Close the lid and cook for 10 minutes. If using a gas grill with multiple zones, decrease the middle flame to low. After 10 minutes, turn the birds over, replace the brick and continue to cook until a thermometer inserted into the thigh reaches 170 degrees F, approximately 8 to 10 minutes. Remove to a cooling rack and allow the bird to rest for 5 minutes before serving.