First prepare the brine. Pour water in a large saucepan and bring to a boil, then remove from heat. Add the remaining brine ingredients and stir until the sugar dissolves. Set aside and let it cool to room temperature.
To make the dough, place all the dry ingredients in a large bowl and mix to combine. Strain the brine through a fine sieve into the dry ingredients and discard any strained solids. Combine with a spatula to develop the gluten (no need to knead the dough), and let it rest for 10 minutes for the liquid to absorb.
Lay an 18-inch-long sheet of aluminium foil on a work surface, put the dough directly on the foil and form it into a round mass. Lift an edge of the foil over the dough and begin rolling it into a cylinder while pinching the ends closed. Twist the ends tightly to seal and bend the twisted ends in half to lock them tight. Wrap with a second sheet of foil in a similar fashion.
Preheat the oven to 350°F (175°C). Put the foil package directly on the middle oven rack and bake for 2 hours. Once baked, remove the foil and let the ham cool.
Meanwhile, prepare the glaze. Put the brown sugar, mustard, soy sauce or tamari, and liquid smoke in a small dish and heat until the sugar dissolves. Set aside.
Place the vegan butter in a large skillet over medium heat until melted. Add the whole ham and lightly brown it all over. Transfer to a baking dish and brush with the glaze until evenly coated. Cover with foil and bake for 30 minutes at 350°F (175°C).
Transfer to a cutting board or serving platter for slicing.