Start by prepping the pork—if there’s a large amount of fat on the outside of the pork trim it off so you have roughly ¼” of fat left. Set the removed fat aside* and the pork into a dish that fits it comfortably.
Finely grate the garlic onto your cutting board, sprinkle on the 2 t-spoons of salt, the thyme leaves and anchovy filets. Mince everything together a bit and then start to mash it all into a paste by dragging the flat of your knife across the flavorsome bits, scraping it back up, running the knife through it a bit more, and repeating.
Add the garlicky paste to a small dish and mix with 1 ½ tablespoons of olive oil. Smear this all over the pork, taking care to get into every nook and cranny of the meat. Cover with plastic wrap and marinade in the fridge for 12 – 24 hours.
Allow the pork to sit on the counter for at least 1 hour, but up to 2, prior to cooking so it comes to room temperature.
Set an enameled Dutch oven in your oven with the lid on, and set it to 275°. Once the oven comes to temperature, let the Dutch oven sit in there for about 20 minutes to achieve even heating.
Move the Dutch oven to the stovetop, leaving the lid in the oven to stay warm, and set over medium heat for a few minutes to get really hot before searing the pork shoulder for about 3 minutes on all sides (start with the side of the pork with the fat on it). If the pan seems a little dry add a splash more olive oil to keep everything lubricated, and if any bits of garlic, thyme or anchovy that fall off the pork appear to be burning remove them.
Set the pork aside and discard the fat before adding the remaining tablespoon of olive oil and shallots to the pan. Sprinkle with a bit more salt and cook for just about 5 minutes, until they start to brown just slightly and soften.
Pour in 2 cups of the rosé and ½ cup of water and deglaze the pan. If you want, tie up a bundle of thyme springs and chuck that in, too. Add the pork back to the pan and bring the liquid to a simmer—the liquid should come about halfway up the pork so if it doesn’t add a bit more wine.
Cover the pan with the waiting lid and move the whole thing to the oven for 4 hours, flipping halfway through, and adding more wine if, by flip time, it’s reduced to covering less than a third of the pork.
After 4 hours is up, remove the pork from the pan to a wide and shallow bowl, spoon over a little liquid to keep it moist, and cover tightly with aluminum foil. Set in a warm spot (or thick wooden cutting board) to keep warm. Taste the liquid and add more salt if needed.
Typically I like to strain the liquid through a fine mesh sieve before thickening so I have a smooth sauce, but the choice is yours (you can either do so right into a small saucepan, where you’ll finish the sauce, or add it back to the Dutch oven if you want to shred the pork and add it back to the sauce before serving). At any rate, skim some of the fat off the surface of the liquid and discard. Bring it to a boil while you whisk the flour with about 3 – 4 tablespoons of rosé until totally smooth. When the liquid is boiling, whisk the flour-wine slurry into it vigorously. Let it bubble away for a minute or two, then reduce the heat to medium-low or low to simmer for about 5 minutes, until thickened slightly. This doesn’t end up like a thick gravy, but rather a sauce with some body; if you want something more gravy-like just up the amount of flour, making sure to add enough wine to get a smooth and pourable paste.
Serve the pork shoulder whole, and slice into it at the table (I say slice, though it will fall apart as you do) or shred it into a meaty pile of pulled pork, bathed in the savory sauce.
Served with some baby new potatoes roasted whole and a simply dressed green salad is all you need—that, and more rosé.
*Any fat that you have trimmed off the pork can be rendered down to a liquid (lard) and used for sautéing or cooking later. Chop the fat into small bits and put in a saucepan (one where the bits of fat will be spread more horizontally than piled vertically) and cover with water. Put over low heat on the smallest burner you have. Let it come to a simmer and leave it there. The heat of the water helps soften and melt some of the fat without burning and, once it all evaporates out, lets the fat finish melting down. Keep a careful eye on it once the water is gone and you start to hear gentle sizzling—it can burn in a matter of seconds at this stage. Once the fat is melted and the solid bits are browned remove it from the heat and strain through a fine mesh sieve. It freezes incredibly well.