Globalising topics such as these doesn't mean writing in non-white history where there is none (although the Cold War? Come on that affected way more non-white people than it did whites). It means taking a step back and looking at history from beyond the confines of the nation-state or Europe to see how they connect to the rest of the world.
Take for example the Irish War of Independence 1919-1921. More traditional approaches would focus almost exclusively on events on our two islands, looking at the impact of British policies and the rise and impact of nationalism locally. Some of the more ambitious studies may consider the impact of the Irish diaspora in places like America and Australia.
A global approach would consider the rise of Irish and Ulster nationalism in relation to nationalism across the globe. It would look across the British Empire and beyond to see what other people thought of events in Ireland, how it impacted upon them, and how their thought and actions impacted upon Ireland. It would note, for example, that at the very same time the war in Ireland was raging, the British Empire also faced uprisings or protests in Egypt, Palestine, Iraq and India. So it would look for the connections between these events (no good historian would assume it all to be a coincidence), how they impacted on each other and try to conclude with an idea of what all this means for the Irish war and the place of Ireland in the world in general.
