Remove all but the bottom rack from the oven and preheat to 425 degrees F. Set a large ovenproof skillet on a baking pan.
Mix the coriander, paprika, lemon zest, 1 teaspoon salt and a few grinds of pepper together in a small bowl. Pat the chicken dry and sprinkle the spice mixture all over the chicken and inside the cavity.
Pour about 1/2 cup of the beer into the skillet, then insert the open can into the larger chicken cavity. Set the chicken upright on the can in the skillet. Add 1 cup of water to the beer in the skillet.
Transfer the baking pan with the skillet to the oven and roast until the chicken is golden brown all over and an instant-read thermometer inserted into the center of the breast registers 160 degrees F, 1 hour to 1 hour and 10 minutes. Carefully transfer the chicken with the beer can to a cutting board and let stand 10 minutes.
Meanwhile, pour the contents of the skillet out into a fat-separating measuring cup (be very careful, the skillet's handle will be hot). Spoon 1 tablespoon of the fat that has risen to the top onto the skillet. Set the skillet over medium heat and add the shallot. Cook, stirring occasionally, until softened, about 3 minutes. Add the flour and cook, stirring, 30 seconds. Pour the juices from the measuring cup into the skillet, leaving the remaining fat behind (if you don't have a fat-separator, pour the juices into a bowl and remove as much of the fat as possible with a small ladle). Bring the juices to a simmer in the skillet, about 1 minute, then add the cream and bring back to a simmer, about 1 minute. If the sauce seems too concentrated, dilute with a little water. If it seems too thin, simmer until reduced to a nice coating consistency. Stir in the parsley.
Remove the can by placing tongs around the edge of the neck cavity and tipping the chicken back just slightly. Carefully twist and remove the can while holding the chicken back with the tongs. Return the chicken to the middle of the cutting board and carve into pieces. Serve the chicken with the sauce.