Selectively applying nested filters on a single column?

Is there a way to ignore part of a filter on a column?

If I have a Date Slicer on a report that is being used to select a subset of dates being displayed on a matrix with date on the rows, can I write a DAX expression for a measure that returns the minimum date specified by the slicer?

If I use just 

MIN(Table[Date])

Then I get the date of each row in the measure.

If I use

CALCULATE(MIN(Table[Date]), ALL(Table))

then this shows the minimum date of the table disregarding the constraints of the slicer.

As a more concrete example, if I have a table containing rows for every date in 2016, then a date slicer on the report restricting this to just the month of November, a matrix shows rows for each day in November. Can I write a measure that shows 2016-11-01 for each value in the matrix?