I am a chef :)
9 years behind the apron and proud of it :)
Yes, you can make a roux with olive oil half and half with butter, but i highly reccommend turning your butter into clarified butter, or what the indians would call Ghee.
Simmer a block of butter in a pan and let it simmer for several minutes. Turn the heat off and leave for a few mins. Then with a ladel, take out the clear gold ghee and discard the fat and salt that seperates.
Now that you have clarified butter, you can put this on the heat in a pan to ridiculous temperatures, and the butter will not burn, nor will it boil.
put half in a pan with half olive oil, leave to heat up to a high temperature. Then add your flour and use a maurice (spatchelor) and mix constantly cooking throughout. You will know when it is ready to add the hot milk (in a seperate pan) because the roux you have made will keep cooking to the point that it leaves the sides of the pan and no longer sticks. It will look like a lump of dough in the pan that you can move around almost like a lumpy ball.
That is your roux done. To make a bechamel (white roux) have another pan of hot milk simmering, and add ladel at a time to the roux ball, mixing with your spatchelor until it reaches the stage where it becomes whiskable. continue to add milk whisking until it turns into a thick white sauce.
This is now a bechamel.
You can continue to cook throughout for longer to make a veloute' (blonde roux) pronounced vel-oo-tay.
continue even further to make a brown roux called an espagnol (brown roux) taken from the spanish term veal jus.
Commonly in kitchens bechamels are made worldwide as the most popular as it is a derivative meaning your base bechamel you have made can be used for various sauces, for example: bechamel in a pan add grated cheese and macaroni pasta, thats macaroni cheese.
Another example is, a seafood chowder, thin down the bechamel with homemade fish stock and make the rest yourself.
Hope this helps! lol !!!!!