Making a roux has two purposes:
- Coat the flour granules with fat so they are able to dissolve into the cooking liquid without binding up.
- Cook the flour to remove the raw cereal flavor.
When the cooked, fat-covered, flour is introduced to boiling liquid the starch granules swell and explode tangling up the cooking liquid. The cooking liquid is thus thickened and delicious.
If your roux is separating then the starch has not gelatinized. Because you saw this problem in the slow cooker and not in a pot I suspect that you are simply not bringing your liquid to a full enough boil to gelatinize your starch.
I have never seen a roux separate out. The roux should dissolve into the cooking liquid. You might check your ratio and make sure that you don't have too much oil in your roux. Variability in measuring your flour might account for why you see this intermittently.
There's already a question about roux/stock temperature (as well as a recent question that's probably a duplicate). Summary: yes, adding cold liquid to hot roux is good. Additionally, most of what I'm saying is already in the answers to "How to mix a roux with stock". I've gone ahead and tried to address your specific concerns, but I really think thoroughly reading rumstcho's answer there would help you.
Yes, it's also bad if the pan is too hot, and you rapidly cook the roux and boil off excess liquid, leaving something that was briefly wet enough to spread along the bottom of the pan, then a second later dry enough to cook onto the bottom of the pan. This is also one of the reasons it's bad to add too little liquid at once. If it ever dries out, you've messed up.
And yes, you should probably be adding more liquid initially, at the very least enough to wet all of the roux. It's fine if the first batch of liquid gets you something substantially thicker than your end goal, but you shouldn't be just trying to get a slightly wet ball of roux, then a slightly wetter one, and ten steps later have a thick slurry. You want to give yourself enough liquid to work with right away.
Once you've got all that, you need to whisk well. If anything is remaining sitting on the bottom of the pan the entire time, of course it's going to stick.
With respect to your other questions: Spices shouldn't hurt you, and a roux containing significant onions and garlic isn't a normal roux, but I've certainly made tons of thick sauces with all kinds of things mixed into the roux, and had no trouble. Bits of things are just, well, extra bits of things. They don't really interact with the liquid when you add it.
Best Answer
Roux Method
The advantages of the roux method:
It also adds oil or butter to the recipe, which may or may not be an advantage.
Slurry Method
The advantages of the slurry method (which is what the second method is, although it is more typically done with water or stock than milk are):
Disadvantages:
Conclusion
Use whichever you are comfortable with. For fine sauces, roux based may be superior (and certainly more buttery), but you can have excellent outcomes with a slurry. For casual cooking , I tend to use a slurry, saving roux for more formal dinners and fancier dishes like Thanksgiving gravy.