In a medium skillet, heat oil and 4 tablespoons butter over medium heat. Add shallots, and saute until translucent, about 4 minutes.
Add morels and chanterelles, and saute until liquid is released and evaporated and they are tender, 10 to 12 minutes. Add Madeira; scrape up any bits on bottom with a wooden spoon. Add stock, salt, and pepper; simmer until reduced by one fourth, about 5 minutes.
Stir in tarragon and cream; simmer until slightly thickened. Reduce heat to low. Add remaining 4 tablespoons butter; stir. Meanwhile, bring a large pot of water to a boil; add salt. Add tortelloni in batches of 12; cook until al dente, about 5 minutes, and remove with a slotted spoon. Divide tortelloni among bowls; spoon sauce over them. Garnish with Parmesan and tarragon; serve.
Three ounces dried morel mushrooms can be substituted for fresh. Set in boiling water, and let rest for a half hour; drain and use.