I'm using a gauge with a crescent tipped blade, and have the bevel facing the stock.
The width of the blade is marked from the gauge line, towards to end..
Use the marking gauge to gauge a depth line approximately a quarter to a third the board's thickness.
This is ideal territory for the router plane, taking thick shavings between the sawn walls of the groove.
Paring the waste with a narrow chisel, held almost horizontal will work just fine.
In either case, work from both sides towards the centre to avoid breakout.
If your preparation was sound, then the two components should sit square.
The faint gauge marks can be planed off with a couple of shavings.
Now watch the video: