Put the wine, vinegar and shallot into a saucepan big enough for you to fit all the ingredients plus the head of a whisk. (Speaking of which, try to use a smaller whisk; one of those giant balloony ones might miss all the corners of the pot.) Set it over medium-high heat and let it bubble briskly, reducing it to a syrupy consistency (until it's about 2 tablespoons).
While the liquid is reducing, cut the butter into ½-inch pieces. If it's very cold, let it sit out—you want it a bit cooler than room temperature when you start whisking it in. But if it's softening or melting, get it back in the fridge or freezer pronto, s'il vous plait.
When the reduction is ready, remove the pan from the heat and turn the flame down to the lowest setting. Add 6 or so chunks of butter and whisk them in. It should look like it's dissolving into the sauce, making it look creamy, not melting and separating into a yellow, oily slick. If it's doing that, add in a bunch more butter and whisk away. What's happening is that it's too hot and the butter is melting more quickly than you're able to emulsify it into the reduction. Adding more cold butter will help to cool it down.
When the mixture is looking creamy and all the butter you've added is incorporated, put the pan back on low heat and continue to whisk in the rest, a couple of chunks at a time. (If you're really a star, you can ditch the whisk entirely and just swirl the pan as you add butter. It makes you a little cooler, but I'm not sure it makes the sauce any different.)
When all the butter is completely incorporated and the sauce looks smooth, season it to taste with salt and pepper and, if needed for perfect balance, a squeeze of lemon or maybe a little more butter. Feel free to strain out the shallots, but I never do.
Notes:
