Mian Mir was a Qadri Sufi of Lahore, born at Sehwan in Sindh, whose following included Mughal princes and whose most famous disciple was Dara Shikoh, Shah Jahan's eldest son.
Sikh tradition holds that Guru Arjan Dev Ji invited him to lay the foundation stone of the Harmandir at Amritsar in 1588, and that he did.
The claim is contested. It appears in Sikh sources of the eighteenth century and later and not in the earliest ones, and some historians hold that the foundation was laid by the Guru himself. It has become politically loaded, cited as evidence of intercommunal harmony and disputed as a later addition.
What is not disputed is the friendship: Mian Mir is recorded as having attempted to intervene with Jahangir on Guru Arjan Dev Ji's behalf in 1606.
His shrine at Lahore is a major dargah and the Mian Mir cantonment area is named for it.
This site records the claim, the dispute and the reason both matter, which is more useful than picking a side.
Dara Shikoh wrote about him in the Sakinat-ul-Auliya, and the Qadiri line at Lahore ran through him to Mullah Shah Badakhshi, who taught both Dara and Jahanara. The prince who had the Upanishads translated into Persian and lost the succession to Aurangzeb came out of that circle.
The earliest Sikh source that has a Muslim laying the stone is a long way after the event and the earliest accounts do not mention it at all. That is what a contested tradition looks like from the inside, and saying so is more useful than deciding it.
The dargah stands in a part of Lahore that took his name. It is visited constantly and almost nobody who visits it has heard the Amritsar claim, which is made and argued about entirely on the other side of the border.