It is totally possible to implement it with the help of the renderCalendarHeader option. You’ll need to create the custom markup and logic for it.
This option takes a function that should return the desired markup. In your case instead of using the built-in mbsc-calendar-nav element, you’ll have to add those two dropdowns and handle the value change manually.
When those dropdown values are changed you can use the navigate method to navigate the calendar to the selected month/year;