Scoop the diced potatoes into a microwave-safe bowl, sprinkle with a couple of tablespoons of water, cover with plastic wrap (poke a couple of holes in it to allow for steam to escape) and microwave on full power for 3 minutes. Before you hit the start button, poke a hole in the side of each garlic clove, put in a small bowl, cover with water and microwave alongside the potatoes.
Heat a very large (12-inch) skillet over medium-high heat. When hot add the olive oil (it should be enough to coat the bottom of the pan heavily). Lay the fish portions in the oil, skin-side down (feel free to make several shallow scores in the skin-side to ensure that it lies flat). Press them gently flat for the first several seconds they are in the pan. Cook until richly browned underneath, 3 or 4 minutes, then flip and cook for a minute on the other side. Remove to a plate, crispy skin on top.
Tip off the water from the potatoes, then scoop them on to paper towels. Roll them around on the paper towels until dry.
With the skillet over the heat, add the potatoes and stir around regularly until richly browned, about 3 minutes. Empty in the can of tomatoes. Remove the skin from the garlic, then finely chop the two cloves and scoop them into the pan along with the olives, jalapeños and parsley. Let cook until nearly dry, then add the broth, reduce the heat to medium and let simmer for a few minutes longer. Taste and season with salt, usually about ½ teaspoon.
Spoon a portion of the sauce into a deep plate and top with a portion of the crispy-skin salmon.