Upon arrival at the 15 DME fix on a heading of 350°, which entry procedure is recommended for the hold?

A direct entry is the recommended procedure for the hold when arriving at the 15 DME fix on a heading of 350°. This is because, when you are inbound to the fix and your heading is aligned with the course to be flown in the hold, a direct entry requires the least amount of maneuvering.

In a hold, the aircraft will typically remain within defined airspace constraints, and to efficiently join the hold, pilots assess their current heading relative to the holding pattern's orientation. Since you are approaching the fix on a heading of 350°, which is aligned with the outbound holding leg, simply turning to enter the hold can be done straightforwardly without needing complex maneuvers often associated with teardrop or parallel entries.

In contrast, the teardrop entry generally involves a turn away from the holding course and then rejoining it, while the parallel entry involves a procedure to fly the opposite direction first before entering the hold. Given that your approach to the fix allows you to make a direct turn to enter the hold without excess maneuvering, direct entry is the most efficient choice.