Reflection?
I have no personal interest in a planet that glows with its own light. Planet Las Vegas not necessarily withstanding.
I was speaking of the light the hypothetical planet reflects from its parent star. The refracted and reflected starlight should have a very small but perhaps measurable Doppler shift as it revolves around in its orbit.
If we were looking specifically for those time-shifted frequencies, rather than light in general, it might be possible to resolve a distant earthlike planet.