This inspired St Bernard to author what is now known as the Prayer to the shoulder wound of Jesus:
"O Loving Jesus, Meek Lamb of God, I, a miserable sinner, salute and worship the most Sacred Wound of Thy Shoulder on which Thou didst bear Thy heavy Cross, which so tore Thy Flesh and laid bare Thy Bones as to inflict on Thee an anguish greater than any other wound of Thy Most Blessed Body. I adore Thee, O Jesus most sorrowful; I praise and glorify Thee and give Thee thanks for this most sacred and painful Wound, beseeching Thee by that exceeding pain and by the crushing burden of Thy heavy Cross, to be merciful to me, a sinner, to forgive me all my mortal and venial sins and to lead me on towards Heaven along the Way of Thy Cross. Amen."
It's a beautiful prayer and story. But one might wonder why St Bernard was thinking about this in the first place. Why would such a detail, which seems to have little theological value, matter? Only a person dwelling on the fullness of the event of Christ's passion for it's own sake would consider asking such a question.
The truths of the Christian faith, whether they be regarding the nature of the Trinity or of Christ, regarding the great events of salvation history, or regarding the very Gospel itself, are great mysteries. They propose to encompass all of reality and to be the singular source of true meaning of all of human life. Their profundity cannot but envelop the seeking soul in awe and warrant our life-long contemplation.
In other words, one does not just 'get' the Trinity and then move on.
Contemplation, on the other hand, pervades Catholic life. St Bernard may have been exceptional in his holiness and love of God, but the contemplative nature of his spirituality was not.
The foundations of Catholic life and worship, the Mass and the liturgical calendar, both in their own way re-propose the work of salvation for our contemplation on a regularly basis for all Catholics.
The Stations of the Cross - in which one slowly contemplates 14 moments in Christ's passion, including Jesus meeting various people along the way and falling with the cross - and the Rosary - which invites us to meditate, one by one, on 20 seminal moments in the lives of Jesus and Mary (e.g. the Annunciation, the Transfiguration, the Resurrection, etc) - are probably the two most widely known and practiced Catholic spiritual devotions.
There are also devotions to the Holy Face of Jesus, the Holy Name of Jesus, the Sacred Heart of Jesus, and to Divine Mercy. The ancient practice of lectio divina - in which one prayerfully reads and contemplates the Scriptures - contrasts sharply with the evangelical practice of reading the Scriptures almost exclusively for personal application. Icons are not intended to be merely portraits so much as highly symbolic portals to the heavenly for our contemplation. Grand cathedrals are built not simply as large gathering spaces but as monuments that point our minds to heavenly things.
All invite us to contemplate, not just know more about, some aspect of the Christian faith in a deeper way.
I am not aware of significant practices among evangelicals that would compare. I can only note that it seems as though some in the emergent church's new monasticism movement are starting to recover some of these elements of Catholic spirituality that were rejected in the Reformation.
The mysterious begs our contemplation. And nothing is more grand, more wonderful, or more mysterious than the Gospel.