Directions for Sauce
1. To make the piperrada, preheat the oven to 450°F. On a large baking sheet, toss the bell peppers and the cubanelle pepper, if using, with 1 tablespoon of the olive oil and season with salt. Spread the peppers apart on the pan and roast for 20 minutes, or until the skins are nicely charred on all sides, turning once or twice as needed. (You can char the skins more quickly under the broiler or by grilling them; however, I discourage this, as roasting for a longer time makes them sweeter and more tender.) Remove the peppers from the oven and transfer to a bowl. Cover the bowl tightly with plastic wrap and set aside to cool.
2. While the peppers are cooling, in a sauté pan over medium-high heat, combine the remaining 2 tablespoons olive oil, the onion, and the garlic and cook, stirring occasionally, until the onions begin to brown and char slightly. Add the oregano and season with salt and pepper. Pour in the wine and deglaze the pan, scraping up any browned bits from the pan bottom. Stir briefly until the wine has evaporated. Remove from the heat and set aside.
3. Unwrap the bowl of peppers and peel them, working over the bowl to capture all of the juices trapped inside the peppers and from the condensation in the bowl. Discard the stems and seeds and slice the peppers. Add the roasted peppers and sliced cherry peppers to the onion mixture in the sauté pan and return to medium-high heat. Strain the pepper juices left in the bowl to remove any seeds and skins, and add the juice to the pan. Simmer until the liquid is reduced by half, then stir in the cherry pepper brine. Taste and adjust the seasoning. Keep the piperrada warm in the pan until the pork is ready. (Or you can store the piperrada, in an airtight container in the refrigerator, for up to 3 days and warm it gently when you’re ready to use it.)
4. Season the pork chops with salt and pepper on both sides. Heat a cast-iron or other heavy-bottomed sauté pan over medium-high heat for 2 minutes. Add the olive oil to the hot pan and then the chops. Cook until deeply caramelized on the first side, 4 to 5 minutes. Flip the chops and add the butter, swirling the pan to help it melt. Add the garlic cloves and thyme sprigs, tucking them around the pan.
5. Raise the heat to high. When the butter foams, baste the pork by tilting the pan towards you so that the butter pools and rapidly, repeatedly spooning the foaming butter all over the chops. Cook for 4 to 5 minutes longer. The chops are done when an instant-read thermometer inserted into the thickest part of a chop registers 145° to 150°F, or use the thumb test; they should be warm, but not hot, in the center. Transfer the chops to a plate, tent with aluminum foil, and let rest for 5 minutes.
6. To serve, slice the chops or dish them up whole. Pile the pipperada on top and serve immediately.
Directions for Broccoli with Anchovies
1. Preheat the oven to 425°F.
2. If you have a very large, ovenproof sauté pan, big enough to fit all the florets in a single layer, heat that on the stove top over medium heat for 3 minutes. If you don’t have a pan that large, place a baking sheet in the oven for 10 minutes. (Preheating not just the oven but also the baking sheet will increase the likelihood of achieving a pleasing char.)
3. While the pan is preheating, in a large bowl, toss the broccoli with 2 tablespoons of the olive oil and season with salt. Dump the broccoli into the preheated pan or baking sheet and roast in the oven for 12 to 16 minutes. The timing will depend a bit on how large your florets are—ideally the broccoli is charred on one side, still fairly bright green on the remaining sides, and just tender in the middle.
4. While the broccoli roasts, make the sauce: Chop the anchovies into fingernail-sized pieces (Use 4 or up to 6, depending on how much you like anchovies). Set aside. In a small pan over medium-low heat, combine the remaining 2 tablespoons olive oil and the garlic. Toast the garlic, stirring, until the edges are lightly browned, about 1 minute. Add the chile and cook for 1 more minute. Remove from the heat and stir in the anchovies. Cover the sauce to keep warm and set aside.
5. When the broccoli is done, transfer to a serving bowl and toss with the anchovy sauce. Serve immediately, or let the broccoli marinate and the flavors intensify, and serve at room temperature. (This dish is great cold the next day as well; just give it a few minutes to temper so any oil that has congealed can warm slightly.)