"Sofrito" is the commonly used word here for sofrito.To the traditional sautéed (it's the best english? word I could find to translate sofregit/sofrito) I added a glass of vi ranci, a kind of oxidized wine very common in catalan cook, and a bit of ginger powder, a combination I like very much, resulting in a sort of sweet and sour contrast. The center laurus nobilis leaf it's added at the end for aromatizing purposes.
Jerusalem artichokes are wonderful, but they can have a rather loud side effect. There was a restaurant in Arizona we used to go to regularly, and they had a roasted Jerusalem artichoke and wild mushroom dish that was amazing. But our wallpaper would start peeling off.
That said, I'd be delighted to eat your dinner.
BTW, I did make my version of the mushroom paella you showed a few weeks back. For the cheese, I used Campo de Montalban given your warning about Manchego taking over the flavors. I was pretty happy with the balance.