The simplest solution is to put a star-shade in the Star-Planet L1 point, thus blocking the starlight reaching the planet.
This is actually a proposal to terraform Venus, by putting a small sunshade that would block enough of the Sun to make Venus cool down. You would still need to fix the atmosphere and probably soil, but putting a giant, ultra-thin film between a planet and its star is surprisingly feasible for an advanced space-faring civilisation.
The problem is, even if you use a shade that blocks only visible light, there is so much energy blocked that the planet will turn into an iceball, even assuming the plants have somehow been switched to infrared or ultraviolet photosynthesis.
To fix this, you have to make your shade from solar arrays, and use the produced energy to feed spotlight arrays on the other side, pointed at the planet. Those will emit infrared and/or ultraviolet in enough quantity to keep the planet hot.
Using solar arrays to feed lights, there will be losses. So the shade will have to be quite a lot bigger than what would be required to only cast a shadow on the planet. Make it two or three times as wide, to account for both losses and downtime of elements for maintenance.
Maintenance will be a big job. Solar arrays, power circuits and lights fail, micrometeorites punch holes in it and break things, radiation and solar wind erode components, and the thing is big enough to be unstable even at L1, so it will need many thruster arrays for station-keeping. But that should be feasible for your advanced civ as long as they are around, or their advanced automated maintenance systems are working.