There is no magic bullet that will do this for us, so what I suggest won't be the only way nor is it comprehensive but perhaps it may serve as a starting point from which you will develop your own way of cooperating with God as He re-forms and rewires our brain to be more aligned with His open and all-embracing heart and mind.
One primary means of becoming more like Him is to spend time looking at Him. Sometimes we call this "contemplation" or "meditation". A primary source of material for meditation and contemplation of God is the Scriptures. We first need to understand what He is like before we can hope to be transformed into His likeness. The New Testament Gospels are some of the best material for seeing what God thinks of us humans, because in Jesus we see God in action. Jesus is the perfect and most trustworthy revelation of what God is like. Taking time regularly to ponder the stories about Jesus, putting yourself in the story and imagining Jesus as he moved among all kinds of people will begin to help you see the beauty of God in the face of Jesus. The more you invest in contemplating His beauty (His nature and character), the larger and more inclusive your heart and mind will grow; in other words, the more you will become like Him (II Cor. 3:18).
If you're interested in more direction about being transformed by looking at Jesus, here is a helpful article about this.
Another practice that can help rewire the brain is a focusing exercise, much-needed in our high tech world with its countless distractions which has resulted in the loss of the ability to focus and listen well. This practice is very simple and involves repetition: pick a one-liner from Scripture (the Psalms is full of short declarations/prayers), and develop the habit of repeating that one short phrase every day several times a day. An example phrase is "I am yours; save me." (Psa.119:94)
If needed, devise a means of reminding yourself to repeat it over and over. Don't be concerned with whether or not you are concentrating on the phrase, simply repeat it whenever you think to do so. The idea is to help the brain learn to focus through repetition; this ability to focus will aid in the practice of looking (contemplating) at God in Christ which in turn will cause us to become more like God and see our world as He sees it.
If needed, devise a means of reminding yourself to repeat it over and over. Don't be concerned with whether or not you are concentrating on the phrase, simply repeat it whenever you think to do so. The idea is to help the brain learn to focus through repetition; this ability to focus will aid in the practice of looking (contemplating) at God in Christ which in turn will cause us to become more like God and see our world as He sees it.
Anything we do to cooperate with God's Spirit requires humility because we will only do this if we acknowledge that we are narrow-minded. I believe that the humble posture of getting under His yoke with Him and learning from His meek heart can lead to having renewed and disciplined minds in which the neo-cortex (reasoning part) of the brain is strengthened and enabled to govern our responses to that which we fear. We can become more objective and look through the loving Creator's eyes rather than through our fear-filled emotions.