To start, heat a medium saucepan over medium heat. Add the butter and minced garlic. Let the butter melt gently, stirring often so the garlic doesn’t brown.
Once melted, take the pot off the heat. Whisk in the flour until the mixture resembles dry crumbs.
Begin adding the milk little by little, whisking thoroughly after each addition so the mixture stays smooth and lump-free. Continue until all the milk has been incorporated and you have a thin, creamy base.
Once all of your milk has been incorporated, the mixture should be extremely runny (and lump-free). You can add the vegetable broth and whisk it in.
Bring the sauce to a boil over medium-high heat, whisking continuously to prevent it from burning.
Once boiling, reduce the heat and allow the sauce to gently simmer until thickened.
When it is nice and thick, whisk in the Parmesan cheese, dried parsley, and dried oregano. Make sure to keep whisking until all the Parmesan cheese has melted.
Once you have a uniform sauce again, season lightly with salt and black pepper to taste. Remember that the Parmesan will add saltiness too.
You can serve your sauce warm or leave it to chill in the fridge.