When I explore this sense of a separate I, I notice that I tend to do it in three general ways.
The main one is to be with the experience of a separate I, to fully allow it - including any resistance to this sense of a separate I, any hopes for it to change, any struggles around it. Fully be with it, allow it, embrace it, as it is. To see it and feel it as it is, here and now (which allows loving it, as it is, to come in as well.)
The second one is to amplify the experience of a separate self. How can I make the sense of a separate self stronger? I find that I do it by tensing up muscles, by strengthening an image of a split between me here and the rest of the world out there, and also by emotions such as anger, fear, desire, and so on. This helps me see how the sense of a separate self is created, and how I do it in my daily life.
The third is to inquire into what is already more true in immediate experience, such as exploring if I am content of awareness, if I am awareness itself, and if the content is anything else than awareness. (Am I any of this content? These sounds? Sights? Sensations? Thoughts? They all come and go, but something does not come and go. What is it that does not come and go? It is awareness itself. Am I this awareness? If I find myself as awareness, I notice that its content arises as a seamless field. What appeared as inside and outside, when I took myself to be a part of the content, is now all a seamless field of no real inside or outside. Where is the boundary between awareness and its content? Does the content appear as anything else than this awareness? The content of this awake emptiness arises as nothing other than awake emptiness itself.)
Together, there is the full allowing of a sense of a separate self, including any associated resistance. There is an active exploration of how the sense of a separate I is created. And there is an exploration of what is already more true in immediate awareness.