Make the marinade. In a small bowl, break up the achiote paste with the back of a spoon, then little by little work in 3 tablespoons of the vinegar and 3 tablespoons of the oil.
Roast the potatoes and marinate the fish (or eggplant). Heat the oven to 400 degrees. If your potatoes are about 1 inch in diameter, cut them in half; if larger, cut into quarters. In a bowl, toss the potatoes or sweet potatoes with about 1/3 of the marinade; if using sweet potatoes add an additional tablespoon of oil. Sprinkle generously with salt, then spread on a rimmed baking sheet and slide into the oven. Roast until cooked through, about 25 minutes. When they are done, the dish should be coming to completion; keep the roasted potatoes on the stove top and the oven on so that you can give them a quick reheat at serving time.
If using eggplant, cut off the top and bottom, then cut thin slices off the two vertical sides. Cut what remains into 4 even planks. Smear another 1/3 of the marinade over both side of each fish fillet or piece of eggplant. Sprinkle both sides with salt.
Roast the peppers. Over an open flame or close up under a broiler, roast the peppers, turning them regularly, until evenly blackened on the outside. Cool until handleable. Rub off the blackened skin, pull out the stem and seed pod, briefly rinse to remove stray seeds and skin, then cut into ¼-inch strips.
Sear the fish (or eggplant), make the escabeche. Heat a heavy, very large (12-inch) skillet (preferably cast iron or nonstick) over medium-high. With a spoon or spatula, scrape excess marinade from the fish or eggplant (there should just be a light even coating). When the pan is hot, add the remaining 3 tablespoons of oil, wait a few moments until the oil is shimmering hot, then lay in the fish fillets or eggplant planks. Let sear until browned underneath, about 2 minutes, then flip and sear the other side. Remove to a rimmed baking sheet. Return the pan to the heat and add the sliced onion. Cook, stirring regularly, until richly browned, about 8 minutes. Scrape in the rest of the marinade and stir for a minute or so, until thick and darker, to remove the raw taste of the achiote. Add the broth and the roasted peppers and bring to a boil. Taste and season with 1 or 2 of the remaining tablespoons of vinegar and with salt, if you think necessary. Reduce the heat to medium-low and nestle in the fish or eggplant. Let simmer gently until the eggplant is fully tender or the fish is as done as you like—anywhere from 1 to 4 minutes. (For me, most fish is good when cooked to medium—it will give slightly when a finger is pressed firmly on it.)
Serve. As the escabeche is coming to a boil, slide the potatoes into the oven again to reheat. Use a metal or silicone spatula to slide a piece of fish or eggplant on deep dinner plates. Scatter a portion of potatoes around the fish, then spoon on the escabeche. Scatter on cilantro or mint leaves and you’re ready to serve.