Switch Instant Pot on to Sauté medium. Add about 1 dessert spoon butter and 2 dessert spoons olive oil. When hot, add the partridges on their backs and allow to brown, then turn onto one side to brown and when well browned, turn to the other side then remove and set aside.
Add the onion and saute until softening, then add the mushrooms,
Cover with glass lid until the onion and mushrooms soften - allow the mushrooms to give off quite a lot of liquid, which is part of the liquid needed to bring the pot to pressure.
Deglaze pot well.
Put the partridges back in the pot, snuggle down among the mushroom mix.
About 2 tablespoons of chicken stock (enough to bring the pot to pressure - it needs to be covering over the bottom of the pot about half a centimetre deep).
Set to Pressure Cook/ Manual, 16 minutes (18 if they are big birds).
When the time is up, do natural release and remove the birds to a hot serving plate.
Switch the Instant Pot to Sauté medium again and add salt and pepper to taste, the tarragon, and the cornflour mixed with the extra chicken stock (or you can reduce until the remaining stock is syrup-y and not use cornflour)
Stir until thickened, stir the cream through and heat (add 2 teaspoons dijon mustard at this point if you like it - I much prefer the sauce with it) then pour over the partridges.
Serve and enjoy! Lots of napkins will be needed, or kitchen roll, as fingers are essential to get the meat off the birds!!