Look Cleats on Sizes 38 and 39
Sizes 38 and 39 of the Monarch shoe require a 3mm spacer to be used with Look cleats, including with Garmin Vector pedals. Here are two sources:
Specialized - either the KEO or SPD SL stackers will work. These come in a two-pack so you should only need to order one. Place 1 x 3mm spacer between each Look cleat and the sole.
Shimano - You will need to buy 2 of these and use 1 x 1mm and 1x 2mm stacked under each Look cleat.