How do I sort my column headers in Power BI matrix visual to start on Monday?

To sort Matrix visualizations (and slicers) we need to use the "Sort by column” feature to sort our original (display) column, by another (index) column. Modify your table to include an index column like this: 
 

Date = ADDCOLUMNS(
    CALENDAR(DATE(2023,1,1),DATE(2023,12,31)),
    "Year",YEAR([Date]),
    "QuarterNr",QUARTER([Date]),
    "Quarter",FORMAT([Date],"\QQ"),
    "MonthNr",MONTH([Date]),
    "Month",FORMAT([Date],"MM"),
    "DayNr",WEEKDAY([Date],2),
    "Day",FORMAT([Date],"DDDD"),
    "DayIndex",IF(FORMAT([Date],"w")="1","7",FORMAT(WEEKDAY([Date])-1,"####"))
)

Then selecting the “Day” column, going to “Column tools” in the ribbon, and selecting the “Sort by column” button, then under that menu selecing “DayIndex”/whatever column you want to sort the display column by.  

Hope this helps.