I guess proofing has some contested definitions — some people refer to the process of dissolving and activating your yeast as proofing, whereas others refer to anything involving letting the yeast rest and do its job as proofing.
When your dough is resting, the yeast is at work eating up the sugars and creating a CO2 byproduct (fermentation), which is what makes the dough rise. (If you overproof your dough, the CO2 pockets will begin to deflate, yielding dense breads with poor crumbs.)
Under- and over-kneading dough really has to do with how strong the gluten bonds that you’ve formed have become. In under-kneaded dough, the gluten has yet to fully align and create the rope-like bonds. It tears easily, but if you keep working it, you can knead it back together and create the missing gluten bonds with little effort. In over-kneaded dough, the gluten bonds are so strong that there is little give in the dough — it’s not really stretchy, it doesn’t hold shape well, and it tears easily. For lack of a better term, over-kneaded dough is sort of brittle.
Here’s my analogy for gluten bonds:
Under-kneaded dough is like a messy pile of unspun fiber. All of the elements for a strong yarn are there, but they are not yet arranged in a way that will inevitably strength them. As you work your dough, the gluten bonds begin to come together and strengthen them like a single strand yarn — this is much stronger than the unspun fiber, but it’s still pretty easy to break the yarn and then spin it back together if you need to do so without anyone being the wiser (under-kneaded dough). As you continue to work, it’s like you’re spinning together multiple strands to create a 4-ply yarn. It’s much stronger now, and it holds its shape. If you tear it, you can get it back together with some effort, but there will probably be a noticeable scar from where the “damage” happened (properly kneaded dough). If you over-knead the dough, it’s like trying to work with climbing rope. It’s tough and if you cut or tear it, you’re screwed — there’s no way to get it back together again. You can’t make the rope less strong, and there is no way to repair the damage that has occurred (over-kneaded dough).
In properly kneaded dough, you should have fairly visible, strong bonds. The dough generally prefers to be “stretched” in a certain direction, but it’s still flexible (and has more “give” or “stretch” when warmed to room temperature). A properly kneaded dough ball should be pretty smooth, but you should also be able to see some of the gluten bonds’ directionality or strata on the surface.
Anyway, any toughness in your dough could be due to:
- under-proofing (not enough CO2)
- over-proofing (CO2 escapes the dough)
- over-kneading (causing the gluten bonds to over-develop and potentially tear)
I usually ignore suggested knead times and just go based on feel. (If you’re using a stand mixer, I have no advice to offer you other than to ditch it and get your hands dirty.) The more breads you make, the easier and more intuitive the process will become.