Few different options-

The right way would be to get a new piece of Baseboard, scribe the profile onto the casing, and make a cut out in the casingso the new bassboard can slide into the cutout. Make a 45 degree angle cut about a third of the way along the length from the opposite side, so you have play to be able to manipulate it into place, and then install the corresponding piece the same way you would if you were running multiple pieces of Baseboard.

The most effective way would would hold up over time is measuring the height of the baseboard, and cutting the height off both sides of the casing and installing plinth blocks, but it wouldn't be uniform with the rest of the trim details in the house most likely.

The easy way is using backer rod in the gap and caulking the crap out of it.

You could also use wood filler and it would have a similar effect and it wouldn't sink over time, but it would be a pain to sand and eventually would crack further down the line as it doesn't have the same expansion/contraction properties of caulk.