In a small bowl, stir together the baking powder, paprika, lemon zest, sugar, 2 tablespoons salt and some pepper. Set aside.
Remove the giblets from inside the chicken. Rinse the chicken with cool water, inside and out, and pat dry with paper towels, inside and out.
Sprinkle the chicken evenly with the salt mixture. Place chicken in the refrigerator, uncovered, for 12 to 24 hours to dry brine.
Place an oven rack in the lower third of the oven; remove the other racks. Preheat the oven to 400 degrees F.
Pour about half of the beer into a glass--and drink it. Place the half-empty can on a baking sheet or roasting pan and drop the garlic cloves into the can. Place the chicken on the can so it's "standing." (If you're cooking for a crowd, this is a good way of roasting more than one chicken at a time.)
Bake until an instant-read thermometer registers 165 to 170 degrees F when inserted into the thickest part of the thigh, 75 to 90 minutes.
Allow to rest, covered in foil, while you make the Beer Gravy. Reserve 1/2 cup of the pan drippings for the gravy.
Carve the chicken and serve with Beer Gravy.
Melt the butter in a medium saucepan over medium heat. Add the flour to make a roux: cook, stirring constantly, until the flour is slightly brown. Whisk in the brown sugar to combine. Add the chicken stock, beer and drippings and whisk to combine.
Add the soy sauce, Worcestershire and horseradish and whisk to incorporate. Season with salt and pepper. Bring to a simmer and cook, whisking, until the gravy thickens, about 3 minutes.