Hey David,
This indeed possible but would unfortunately custom coding to achieve 🙁 If you’d like to customize the core widget code directly, that is a customization that’s a bit too far outside the scope of our support forums for us to help very much.
However, some simpler methods might be to just “fake” this effect by having a Mini-Calendar widget and then add the “Upcoming Events” widget below it; then, use CSS to hide the events list in the Mini-Calendar, so that the unchanging “Upcoming Events” widget displays instead. You could achieve this with CSS like this:
.tribe-mini-calendar-wrapper .tribe-mini-calendar-list-wrapper {
display: none !important;
}
You might need further CSS to get the display of things “just right” on your site from there, but this hopefully get you started! 🙂
Cheers,
George