In a large skillet, melt butter over medium heat.
Add garlic, cooking for 30 seconds or so, until fragrant.
Whisk in flour, salt, pepper, and oregano. Whisk to combine well.
Slowly add milk, whisking until well combined. Continue whisking until desired thickness is reached.
Remove from heat, stir in cheese until smooth.
Use immediately or cover and chill until ready to use.