If I am making this dish for a regular everyday dinner I cut the chicken breasts into 1 inch cubes. But if I am serving guests then I leave them whole and serve them with some of the sauce drizzled on top and the rest on the side.
If using fresh mushrooms; slice them.
In a saucepan over medium heat add the butter, olive oil, garlic, fresh mushrooms (if using fresh), onion and chicken. Saute, stirring frequently till chicken starts to brown.
Using a slotted spoon remove chicken from pan. Add the flour to the pan and stir for a minute. Start adding the milk slowly while stirring to prevent any lumps from forming.
Return the chicken to the pan and add the tarragon, bouillon and canned mushrooms (if using canned), salt and pepper. Reduce heat to low, cover and simmer stirring 2 or 3 times till chicken are well cooked and tender; about 30 minutes.
About 5 minutes before serving add the cream and heat back up.
Serve over white rice or pasta with sauce ladled on top.