Don,

If you are positive that you have IE set as your default app
for web browsing then the only thing I can suggest is setting something
else (other than Edge) temporarily to see if that forces things to open
in the chosen browser, then switch it back to IE.

There is no reason for anything other than Cortana initiated
web searches to open in Edge if you have reassigned your default browser
to something else. It sounds like although it's showing IE as your
default that something under the hood didn't actually "take." If
switching it to something else doesn't make the behavior change then I'd
suggest running SFC and DISM (more details later, if needed) to see if
you have some sort of system file damage/corruption that can be repaired.
--
*/Brian/*

*/Here is a test to find out whether your mission in life is complete.
If you’re alive, it isn’t./*

/ /~ Lauren Bacall