Peel and thinly slice the onions.
Thinly slice the mushrooms (stems of button mushrooms are soft and edible so include them).
Melt the butter in a pan. Add the onions.
Cook the onion slices gently just until they start to turn translucent.
Add the sliced mushrooms and stir.
Pour in the rice wine.
Add the tarragon, some salt and pepper.
Cook, uncovered, stirring often. The mushrooms will expel water. You want the mushrooms and onions to soften in the mixture of mushroom water, onion juices, butter and wine.
When the mixture is quite dry, the onion and mushroom slices should have lightly caramelized. Turn off the heat.
Spread the mushrooms and onions over the entire bottom of the pan then cover the mixture with the shredded Colby cheese. Leave for the cheese to melt in the residual heat.
Meanwhile, grill the bread slices.
Assemble the sandwiches.
Lay two grilled bread slices and cover them with shredded lettuce. Top with the roast chicken strips.
Using a small spatula, lift portions of the cheese topped mushroom mixture and lay on top of the pile of roast chicken.
Top the filling with the remaining grilled slices of bread and serve your cheesy chicken and mushrooms sandwich while the cheese is still hot and gooey.