Preheat the oven to 350 degrees F. Line a baking sheet with parchment paper.
Cut each zucchini in half lengthwise to create 2 long pieces. Scrape a small, ideally pointed spoon down the center of the zucchini halves to remove and discard the flesh, leaving about 1/4 inch of flesh intact. Place the zucchini boats on the prepared baking sheet.
Place a saucepot over medium heat and add the butter. Heat until melted, then brush the cavities of the zucchini boats with the butter. Add the chicken stock and reserved hominy liquid to the remaining melted butter and heat until simmering. Whisk in the grits and reduce the heat to medium-low. Cook, stirring occasionally, until the grits have softened and thickened, about 15 minutes. Stir in the pimientos, beans, chives, 1/2 cup cheese and 1/2 cup hominy (save the remaining hominy for another use). Season to taste. Remove from the heat and allow to cool briefly. (The grits will continue to thicken as they cool.)
Sprinkle the zucchini boats with salt and pepper. Spread about 1/4 cup of the grits into each zucchini boat, mounding the filling over the edges. Sprinkle the remaining cheese over the boats.
Roast until the boats have softened and the cheese just starts to brown, 20 to 25 minutes. Sprinkle with the fresh parsley and serve immediately.