MonthGrid[
  finalSpacings:{_Integer,_Integer},
  finalBorderWidths:{{_Integer,_Integer},{_Integer,_Integer}},
  finalOptions_Association,
  titleGridder_Function,
  monthName_String,
  monthSpacings:{_Integer,_Integer},
  monthBorderWidths:{{_Integer,_Integer},{_Integer,_Integer}},
  monthOptions_Association,
  headerCellGridder_Function,
  weekdayNames:{__String},
  dayCellGridder_Function,
  dayOffset_Integer,
  days:{__String}]:=
  DataGrid[{2,1},finalSpacings,finalBorderWidths,finalOptions,
    {titleGridder[List/@List/@Characters[monthName]],
    HeadedGrid[monthSpacings,monthBorderWidths,monthOptions,headerCellGridder,weekdayNames,dayCellGridder,ArrayPad[days,{dayOffset,0},""]]}];

(*A compact example:*)
MonthGrid[{0, 0}, {{0, 0}, {0, 0}}, <||>,
  DataGrid[{1, Length@#}, {0, 1}, {{1, 1}, {0, 0}}, <||>,ToUpperCase@#] &,
  "September", {0, 1}, {{0, 0}, {0, 0}}, <||>,
  DataGrid[{1}, {2}, {0, 0}, {{0, 0}, {0, 0}}, <||>, #] &,
  {"Su", "Mo", "Tu", "We", "Th", "Fr", "Sa"},
  DataGrid[{1}, {2}, {0, 0}, {{0, 0}, {0, 0}}, <|"alignment" -> {-1, 1}|>, #] &,
  2, ToString /@ Range[31]]//AsString