roux won't thicken

Note that flour-thickened sauces become thicker as they cool. The cooking step is for flavor, not thickening, to keep the finished sauce from tasting like raw flour. Overcooking, however, will diminish the flour's thickening capability so that's one possibility and if the flour formed clumps in the bottom of the pan as can happen using the technique described, that's another possibility. One method to recover from the situation would be to make a slurry of corn starch in a small amount of cold water and add it to the simmering sauce (as per the first post, just a little bit at a time).

My best solution for this is as follows (works for any sauce that needs thickening and can deal with butter): Take some softened butter and mash an equal amount of flour into it until it forms a thick paste (so 2 TB of flour for 2 TB butter). Stir the paste into the sauce. As the butter melts the flour will thicken the sauce and this way you won't get lumps. If your butter is cold, you can always work the flour in with your fingers but make sure it is pasty and not lumpy and that all flour is worked in. Good luck!

I'm sorry but that description is not a "roux". Any vegetable content should not go in until the roux is already made. Your roux is fat (or oil) and flour. Seasoned. Period. It sounds like you are working from a badly scripted recipe.

Perhaps try adding cornstarch, a teaspoon at a time.