Soto-makikomi (外巻込), the outer wrapping throw.

Nage-waza (throwing techniques), Yoko-sutemi-waza (side sacrifice techniques), Gokyo 4th set (Dai-yonkyo).
Required for: 16th Mon (brown belt, British Judo Association); 2nd Kyu (blue belt, JudoScotland); 1st Dan (black belt, British Judo Association); 2nd Dan (black belt, British Judo Association); 3rd Dan (black belt, British Judo Association); 4th Dan (black belt, British Judo Association); 5th Dan (black belt, British Judo Association).

About
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Tori wraps uke's arm from the outside, turns in, and winds uke over the body to the mat in a committed rotation.

Step by step (standard right-handed form)
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1. From a right-handed grip, pull their right sleeve firmly across your body with your left hand.
2. Release your right-hand grip and swing your right arm up and over their right arm from the outside, trapping it beneath your armpit against your side.
3. Pivot and turn your back into them as for a hip throw, their trapped arm keeping their chest tight to your back.
4. Wind your whole body to the left and let yourself fall forward and around: your rotation is the throw, and your body travels to the mat with theirs.
5. You land on your left side; they roll over your body and land on their back beside you. Release the trapped arm as soon as they land.

Key points
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1. Trap uke's arm under your armpit as you turn
2. Wind your whole body: the rotation is the throw
3. Roll through onto your side so uke lands beside you

Receiving it
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Your right arm is trapped under theirs from the outside and their whole body turns and falls: you are wrapped around them and taken to the mat together. Your trapped side cannot slap, so curl into their rotation, keep your chin tucked, and let your side and back arrive together as you land beside them. Take this one gradually in practice until the shape is familiar.

VI judo notes
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Releasing the lapel for the wrap is the risky moment, so make it a slide up the outside of their arm and clamp it under your armpit where you can feel it held. From then on that arm is your only connection, so keep it until they land. Learn the rotation with a coach beside you, because you are taking the mat as well.

Reference pages elsewhere
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Soto-maki-komi on the IJF technique reference (International Judo Federation): https://judo.ijf.org/techniques/Soto-makikomi

From Waza Book: https://wazabook.com/techniques/soto-makikomi/