Thanks for highlighting that.
Let’s break that down, shall we?
-Sitting cross leg: Bad for your circulation. Plus it’s different from kneeling.
-Clearing your mind: No. Just no. There are Christian mediation that is close, but never “clear your mind.”
-Focusing on your breathing: Depend on the context.
There is a few Catholic and Orthodox practice that are similar, but distinctive to the Eastern Prayer. The main thing is that it never is about clearing your mind. It’s always with God’s words in mind.
We already had mentioned Rosary. Of course, you have chaplet of Divine Mercy.
There are meditation that start to veer into what on its surface are “oriental mediation”. The most famous one is the Lectio Divino. There is the carmelite spirutality (which i have no clue of) There is also The Prayer rule of St Pachomius, taken up by the Eastern Brethen; a link to one from a Byzatien Catholic church:
stmaryhillsboroughnj.org/files/Prayer/BeginningPrayersPrayerToSanticyTheHours.pdf
The keypoint is always have the Word (note the capital) in mind.