In a large skillet, melt the butter and olive oil over medium heat. Add the minced shallot and garlic, sautéing until softened, about 2-3 minutes.
Add the sliced morel mushrooms to the skillet and cook until they are tender and browned, about 5-7 minutes.
Carefully pour in the bourbon and let it simmer for about 3-4 minutes, allowing the alcohol to cook off and the sauce to reduce slightly.
Stir in the heavy cream and Dijon mustard, bringing the mixture to a gentle simmer. Cook for an additional 5-7 minutes, stirring occasionally, until the sauce thickens.
Season with salt and pepper to taste. Remove from heat and garnish with fresh parsley before serving.