Set a medium-large skillet over medium-high heat, add the oil and butter and when the foaming subsides, cook the mushrooms and rosemary for 5-7 minutes, until tender and golden.
Meanwhile, toss the grated cheese with the flour.
Add the wine, beer or cider to the pan with the mushrooms and bring to a simmer.
Add the cheese mixture in handfuls, stirring to melt the cheese after each addition.
When the cheese is melted and smooth, serve immediately with crusty bread, or warm the skillet in the oven before serving.