In a large, nonstick frying pan (I use Woll fish pan here) pour a little olive oil and, when warm, start frying the fish. They won't need much, but keep an eye - some fillets may be thicker than others - and remove to a couple of warm plates, tented with foil, as they're cooked. I think those look best with the pearly pink skin uppermost.
When all the fish fillets are cooked, add a tablespoon of olive oil plus the dribble of anchovy oil to the pan and stir in the minced garlic and the anchovy fillets. Keep stirring with a wooden spoon or spatula and, as the oil warms, the garlic should soften and the anchovies seem to melt into a sauce. Add most of the thyme leaves, then the sherry. After a scant minute's bubbling, replace the wooden spoon in your hand with a wire whisk or a handheld mixer or electric whisk - one of my favorite pieces of equipment - and, off the heat, whisk in the butter. Pour this amount of viscous sauce over the 2 plates of fish (this is for flavoring, not coverage), then sprinkle with the few remaining thyme leaves. Serve with the chickpeas and tomato salad. I know this sounds like a lot for 8, but I like to work on making enough for half those present to have second helpings. At any rate, I've found that a good rule of thumb.