You're not cooking your roux mixture enough then. Before adding liquids you should cook the roux for a good 5 minutes - it should even stick to the bottom of the pot a little - it comes off when you add the liquids. This gets rid of the raw flour taste. Adding milk is just for consistency now, so no need to cook the thing for ages at all. And adding one tiny bit of milk at a time is an old wive's take - you can add a little at first but then as you go along you can chuck quite a lot in without it going lumpy - the flour is already completely covered in fats and with a whisk it will emulsify well...
No. Let me break it down for you.
Equal quantities of flour and butter. For a litre of sauce I'd use one and a half tablespoons of butter or thereabouts. Maybe two depending on how thick I want the sauce. Melt the butter and leave it to turn a little brown. It will froth up and then when it stops frothing, it will go brown quickly. Don't over-do this - watch it carefully. This is called a beurre noisette, and actually reduces the efficacy of a roux, so rather use two tablespoons of flour for this application.
Then add in your flour and whisk. Continue cooking this mixture for 5 minutes on a medium heat, whisking all of the time. It will begin to dry out and catch a little but this is fine. If it becomes difficult to work with then add a drop of milk. You are cooking the raw flour flavour out now. Then add in a few splashes of milk and whisk. It will thicken up considerably at this point. Continue adding a few splashes of milk at a time until you have what resembles a paste. Now you can start chucking in more and more milk. What you have there is an emulsion already so no need to treat is like a dainty mayo at this point. Now start to add your seasonings. First thing's first - white pepper. One teaspoon at a time until the flavour works for your palate. Then plenty cracked black pepper, but careful of the heat here. Then add in a few whole peppercorns (best soaked in vinegar overnight). In a separate pan, boil off about 75ml brandy. You can flambe it if you like to make the wife's panties wet. Add it to the sauce as well as a few drops of worcestershire sauce, now season with salt. Don't salt beforehand, for science and taste reasons, but season right at the end. The salt inhibits the dispersion efficacy of an emulsion btw.
That's it. Ten minutes tops...
