First wipe the button mushrooms clean with a damp paper towel. Slice the morels in half first and check for bugs that might have crawled inside. If using fresh morels, wash them first; if dried you may reconsititue them by soaking them in warm water for 30 minutes.
Melt 4 tablespoons of the butter in a pan and saute the button mushrooms over medium-high heat for about 5 minutes or until done. Set these aside.
Now melt the remaining 2 tablespoons of butter in the same pan and saute the shallots over medium-high heat for about 4 minutes. Add the sliced morels and sauted for a minute more.
Reduce the heat slightly and deglaze the pan with the wine. Stir in the stock and cream. Add the tarragon and season to taste with salt and pepper.
Let the sauce bubble for a few minutes until it reaches the desired consistency, then add the mushrooms back in and heat through.
Serve with crostini (slices of a French bagette, toasted).