over medium

Prepositional phrase

(US) Of an egg prepared as food, fried on both sides so as the whites are cooked, and the yolks are soft, but not runny.

Japanese Meaning

卵を調理する際の焼き加減を指し、両面を焼くことで白身はしっかり火が通っている一方、黄身は柔らかく、完全には固まっていない状態を意味する。

For breakfast I asked for my eggs over medium and a cup of coffee.

朝食に、両面を焼いて白身は固まり黄身はやや柔らかい半熟の卵とコーヒーを一杯頼みました。

Sense（1）

(US) Of an egg prepared as food, fried on both sides so as the whites are cooked, and the yolks are soft, but not runny.