How to Make It
In a large bowl, combine all of the ingredients. Mix by hand, squeezing the vegetables until the cabbage begins to soften and releases some liquid, about 3 minutes. Pack the cabbage-pepper relish into a 2-quart jar, cover tightly and refrigerate overnight, shaking once or twice.
In a medium bowl, whisk all of the ingredients together and season with salt and pepper.
Light a grill. In a large cast-iron skillet placed directly on the grate, bring 3 cups of the beer to a simmer; it should be at least 1/2 inch deep.
Meanwhile, oil the grate and grill the chorizo over moderately high heat until lightly charred all over, about 6 minutes. Add the chorizo to the beer in the skillet and simmer, turning occasionally, until cooked through, 8 to 10 minutes; add more beer to the skillet as needed.
Return the chorizo to the grill and cook until well-browned, about 6 minutes. Transfer to a work surface and let rest for 5 minutes. Grill the hoagie rolls cut side down until lightly toasted, about 2 minutes. Spread some of the remoulade on the buns and top with the chorizo and relish. Pass the remaining remoulade and relish at the table.