Okay, but to what end?

When humans watch cosmic events, the best we can do for active imaging (illuminating the event in some spectrum rather than just passively receiving the light/radio/neutrinos/whatever) is to shine a laser at the moon or use radio to get a pitiful handful of bits out to probes at the edge of the solar system. If an alien intelligence wanted to observe us observing something, they would have to be able to pick up those reflected non-natural signals to see that there was another intelligence at work.

Conversely, for us to observe aliens observing something, they would have to be lighting it up with enough signal for us to see the reflection/spillover. In our own cosmic neighborhood, we've just started being able to detect entire planets bathed in the light of entire stars. In other galaxies we can't even detect individual stars, we can pretty much only resolve supernovae. Even if aliens could generate an energy beam strong enough for us to detect from another galaxy, why use it to illuminate a stellar curiosity? It would be so energetic that it would likely destroy the object that it was focused on.