When I do a normal counter top rise, shape, rise and then bake with this recipe, my results is my profile picture. It comes out wonderfully.
I decided I wanted to cold proof for that wonderful extra flavor but I am confused at what is happening here. I mix everything together, knead the dough, let it rise the first time, punch it, stretch and pull it a few times, shape it and then place it in the fridge in a bowl covered with plastic wrap. The next day, about 12-14 hours later, I pull the dough out and let it sit on the counter while the oven+dutch oven heats up to 450. I put the dough on parchment, drop it into the Dutch oven, drop in 2-3 pieces of ice down the side, put the lid on and bake for 35 mins. Pull the lid off and bake about 5-10 mins. The bread pretty much stays the same as what it looked like going in as if no spring is happening. It also does not rise much at all while in the fridge.
The only thing I can think of at this point is to pull the dough out reshape it and let it rise again as it warms up and then bake it? Everything I have researched is half and half saying you can bake straight from the fridge or you need to let it warm back up before baking.
When you put dough or a shaped loaf into the refrigerator, it will continue to ferment while it cools down. You can figure on another hour of fermentation in the fridge, or more for a large mass of dough. So your loaf can become overproofed. You need to get it into the refrigerator roughly an hour before it would have been fermented or proofed enough. If the dough is very lively (maybe it's been made with a lot of yeast), even sooner.
A shaped loaf can be baked right from the fridge, or allowed to warm up (e.g., by 1/2 hour). Bulk fermented dough can be shaped and proof right from the fridge, but I usually let it warm up for an hour first. This makes it easier to join seams.
You can also reduce the amount of yeast you use, if you are making a yeasted bread. It will ferment more slowly and the longer fermentation will make it taste better, whether or not you refrigerate it.
Recipes that say to "punch down" - literal punching is not needed. This step, which is really about deflating the dough so it can rise again without overstraining the gluten network, isn't needed and probably should be avoided before shaping a loaf. It's ordinarily used when the dough is going to be allowed to rise a second time before shaping. Handle the dough gently, and degas it a little to get rid of an excess of gas but let it stay airy. You wrote that you stretch the dough, and that along with simply getting it out of the bulk ferment container will probably degas it enough.
If it doesn't work - don't do it. Baking from the fridge (cold) isn't worth it. You can do the same (without the cold sleep) if adjusted for it. Enjoy!
Hard to make a remote diagnosis (as always). Maybe the fridge is too cold. Maybe the bulk fermentation is not long enough. Maybe the final cold proof is too long and/or warm.
Do you have a shot of the crumb? Might help.
I you want to try the cold fermentation because of the taste, I'd try to do bulk cold fermentation. Warm bulk fermentation until you see a bit of activity, then bulk cold fermentation for 12h - 24h (depending on you starter, flour and schedule), take it out of the fridge. Finish the bulk fermentation on the countertop (as usual) as long as needed, shape the loaf and final proof also as usual. Like this you can control both the bulk fermentation and the final proof.
Ok ok, so I think what I was doing is trying to do the final proof in the fridge. When what I had more in mind was bulk cold fermentation as you have mentioned. I will try this for the next bake, thank you!