Into a large, deep skillet over medium-high heat, add the butter and vegetable oil.
When the butter is melted, add mixed mushrooms. Cook for 1 minute.
Add sea salt, ground black pepper, cayenne pepper, and nutmeg. Cook, stirring frequently, 2 more minutes.
Sprinkle with all-purpose flour then gradually add chicken-style broth ¼ cup at a time, whisking after each addition.
Bring just to a simmer then reduce heat to low.
Add sour cream, unsweetened almond milk, and butter. Whisk until thoroughly combined and butter is melted.
Continue cooking, stirring frequently, for about 5 minutes, until sauce is thickened.