The DU Lounge

While the flour is cooking in the butter, enough energy is being used to keep the butter from burning.
1:1 butter to flour. So, 2 sticks of butter, one cup of flour, assuming you're making a batch that needs 2 of the normal size boxes of stock
You don't have to stir continuously, but quite regularly. Medium heat helps, too. Takes a little longer, but safwr.
When the roux starts to change color, it goes from tan to brown pretty quickly. So, a little more attention, a but more stisafer. At this point, we're more worried about charring the "bread" than the butter. Don't want to charge the roux, itsekf.
If the butter scares you, use a veg oil. Given the strong flavors, olive oil might not be a bad choice.
Also, I've hear about cooking a roux in the oven, mixing the flour with microwave melted butter,am & laying it into a cake pan.
But, I forget what oven temperature was suggested, or how much time. Alton Brown does it this way.
I cook with butter a lot, including making brown butter. So, I'm kind of past the butter burning stage. I do it so often, I've got a feel for it.