How do you make buttery oil?
I am not sure what you mean, if you want to fry or saute something in butter flavored oil just add a little butter along with the oil to the pan. If you wanted to make a quantity I wouldn't advise that you do that since the milk solids in the butter would solidify and you would also have a very short shelf life. I do this all the time when I want a buttery flavor and it works quite well.
Reading between the lines here..I think Submitter might be thinking about Ghee, or clarified butter. Which is great for frying fish, or in Indian food. It has a high smoke point unlike 'butter', well it is butter with the milk solids removed.
It keeps very well in a jar at room temp--a couple of months and much longer in the fridge.