Combine the breadcrumbs and Parmesan cheese in a small bowl and set aside.
Melt butter and add olive oil over medium heat. Sauté shallots and garlic in the butter/oil mixture until they are wilted. Add the oysters, herbs and cream and heat until the oysters just start to firm up.
Remove pan from heat. Place oyster mixture in a casserole in a single layer or in 2 individual oven-safe pans. Spread breadcrumbs over the top and broil in the oven for 5-6 minutes until the breadcrumbs are toasted.