Melt half of the butter and add the meat. Sear until golden brown on all sides.
Remove the meat and deglaze the pan with a splash of white wine, scraping out the solidified stock in the bottom with a spatula.
Pour the liquid over the meat and set aside. Return the clean pot to heat, add the remaining butter. Sauté the shallots for 2 minutes, until shiny.
Add the meat, cooking liquid, white wine and bay leaf. Cover, bring to a gentle boil and let simmer for 2 ½ hours.
Remove the lid and continue to simmer for another 10 to 15 minutes, thus reducing the liquid by approximately one third.
Stir in cream, add morels and simmer for another 10 minutes. Season with salt and pepper. Fold in the champagne the very last minute before serving.