Heat a gas grill to 500ºF. Place a brick, wrapped in aluminum foil, onto the grates of the grill to heat.
Add the vegetable oil to 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 cool 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 in 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 digital instant-read thermometer inserted into the thigh registers 170ºF, 8 to 10 minutes. Remove to a wire rack and allow the bird to rest for 5 minutes before serving.