Clean the mushrooms and unless they are quite small, cut each one in half.
Wash and seed the peppers and cut them into approximately 1 inch squares.
Peel and slice the onion.
Prepare the sauce: mix together the mustard, brown sugar with a little wine until you have a smooth paste. Add the remaining wine, season with lots of freshly ground pepper and a little salt. Stir well.
Melt the butter and oil in a large saucepan and saute the onion until it is transparent.
Add the mushrooms and the peppers to the pan and saute for a few minutes, stirring often.
As the mushrooms begin to brown and reduce in size, add the wine sauce.
Simmer the mixture over a low heat, uncovered for about 30 -45 minutes or until the sauce is much reduced and thickened.
Serve garnished with the chopped tarragon.