Getting the last date where a given week day occurred
The most obvious point to make is that whenWasLast repeats the entire code of whenWasLastBasedOnDate. You can (and should) simply write the whole method by just calling whenWasLastBasedOnDate:

let whenWasLast (weekDay:DayOfWeek) =
    whenWasLastBasedOnDate(weekDay, DateTime.Now)


Another point is that you should write AddDays(-1.0) as AddDays -1.0. In languages with ML-like syntax it is generally discouraged to add redundant parentheses around function arguments because it encourages the misconception that the parentheses are part of the method call syntax.

On a somewhat more subjective note, I think that using if would read nicer than a match without any patterns.



On a more general design note it is generally considered good style in functional programming to use higher order functions to express the code more abstractly. For example instead of saying "Check if the given day was a weekDay. If so, return it, if not repeat with the day before" you could say "Look at the last seven days and return the one who is a weekDay". This is not only more idiomatic functional programming, but also makes it impossible to get into infinite recursion by getting the exit condition wrong. In code it would look like this:

[-6.0..0.0] |&gt; Seq.map currentDate.AddDays |&gt;
    Seq.find (fun d -&gt; d.DayOfWeek = weekDay)