Get dimension value based on minimum metric value

thebaguette , Try a measure like

Rankx(Filter(allselected(Table[EAN], Table[Month Year], Table[Store]), [EAN] = Max([EAN]) && [Month Year] = max([Month Year])), calculate(Min(Table[Price])),,asc,dense)

you can use visual level filter of 1

For Rank Refer these links
https://radacad.com/how-to-use-rankx-in-dax-part-2-of-3-calculated-measures