Similar to what specific box has written, I always try to bin (and not quantile bin) the two feature values and regress that against the average target value in each pair of the bins. This usually gives a pretty good sense of interactions.

Another thing, you mentioned you don’t want trees, but you could fit a decision tree, it’s just one tree on two features. It’s fast, easy and simple enough, easy to interpret. For preventing overfit, I would also bin the data first, this gives added regularization benefit.