Step one

In a large stockpot, combine 3 cups water, the salt, and sugar. Bring to a simmer over high heat, stirring until the salt and sugar dissolve. Reduce the heat to medium-low and stir in the honey, chiles, 3 smashed garlic cloves, 1 bay leaf, peppercorns, coriander, red pepper flakes, 1/4 teaspoon pimentón, and the parsley. Remove the pot from the heat and add the ice, stirring until it melts and the brine is cool to the touch, 1 to 2 minutes. Add the pork loin to the brine and submerge it. Cover, transfer the pot to the refrigerator, and brine the pork for at least 6 hours or overnight.

Step two

Preheat the oven to 350°F.

Step three

Remove the pork from the brine and pat dry (discard the brine). Use kitchen twine to tie the pork in 6 to 8 places, making the roast into a compact cylinder. Place the remaining bay leaf in a mortar or spice grinder and pound or pulse until finely ground. Transfer it to a small bowl and add the rosemary, thyme, 6 cloves chopped garlic, and remaining 2 tablespoons pimentón. Stir in the oil to create a thick paste. Rub the paste all over the pork.

Step four

Transfer the pork to a rack set in a roasting pan. Roast until a thermometer inserted into the thickest part of the pork reads 125°F, 30 to 40 minutes. Set the pork aside on a rack to cool to room temperature, about 1 hour. When the pork is cool, wrap it in plastic and refrigerate until chilled through, at least 1 hour or up to 2 days.

Step five

To serve, use a sharp, thin knife to slice the pork as thinly as possible, removing the twine as you slice. Overlap the pork slices to cover the bottoms of four plates. Scatter on the pickled onions, drizzle with olive oil, and sprinkle with flaky salt. Serve chilled.