Here in Argentina that's what we do with the parrilla although we don't use sauces as such it's usually just fat residue that's left.
Mine sits uncleaned till the next time I use it. Once a new session is underway and a good heat has built up I rub it over with newspaper which takes away any old stuff.......haven't had food poisoning yet. :D
The cast iron pan in the house is just left steeping in water then given a rub with a cloth which is usually sufficient......you could do that if you have something big enough to steep it in.

In a restaurant kitchen they scrub the pans and grills with kosher salt or grill bricks after bringing them up to a high temperature. Water never touches them. Keeps the seasoning on and keeps them non-stick. wj

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the same way you clean a real wok...

I was wondering how it was done in restaurants. I was pretty sure they didn't leave the gunk on until the next night!

I'm probably going to borrow a pressure washer from a friend this weekend to blast mine.

I dunno, I've had some pretty good meals at restaurants that had scuzzy looking grills. :D

A successful lesson I learned from a Churrasco (BBQ) in Brasil:

1. Cleaned grill heated.
2. Olive oil sprayed onto grill - somewhat heavy.
3. Grill then used ( Half day/all night ). Charcoal & wood fired, and not gas.
4. Grill continued hot when finished, to char leftover material.
5. Grill scraped with a long handled, brass-wire brush.
6. Grill recoated with Olive oil spray.

The BBQ meats cooked were only coated with coarse rock salt, and no sugar-sauce. There was some fresh pineapple, dusted with Canelle (Cinnamon) and lightly grilled as a simple but delicious dessert item. No residue left on the grill.

Cast iron care/maintenance
 

How do people take care of their cast iron? I have a 12" Lodge skillet I use sometimes. I seasoned it according to this blog post, which does indeed provide a nice hard shiny black layer on the pan. I usually clean it with a soft brush and dish soap. then dry thoroughly, heat on the stove to ensure all the moisture is gone, and rub with a little vegetable oil. But even the soft brush seems to scrape too much of the seasoning off. I now have dull patches on my pan where I scrubbed the burned on bits of steak off of the pan. I have a Lodge chain mail scrubber too, but it didn't seem to do anything to the burned on bits.

I usually use this Serious Eats article as my basis for care and maintenance. I really don't want to keep scraping the seasoning off the pan, though. What do you all do?

I never use soap on my cast iron. I followed the instructions from Kent Rollins to refinish my Lodge cookware which has a very poor machine seasoning finish from the factory.

I also never use soap.

If I can get away with just a rinse, then that's all I do, and then dry, lightly rub with oil, and put into a 350 degree oven for at least 30 minutes to make sure it's really dry and to add to the "seasoning".

If I need to scrub, I use a little chain mail sort of thing I got on amazon to get rid of the gunk, then the above.

Some say use coarse salt to scrub, if you have to, and re-oil.

Once it's well seasoned, you can use a bit of dish detergent occasionally for a big mess like the seared scallops we had tonight. Normally, never soap. Hot water and a nylon scrubby pad, and wipe dry. The only time I ever have to re-oil is if there are several big messes in a row requiring detergent. Maybe once a year. We use cast iron every single day, and for over 90% of stove-top cooking.

Your last sentence is a big part of it. Cast iron is supposed to improve with use. Many families have cast iron that they pass down to future generations. It has never really caught on with me but maybe because I do so much cooking on the grill. Do you use yours in the oven as well?

Sometimes, but not very often. Mrs. braslvr makes blackberry cobbler in a medium skillet, and pita bread on a large very hot one in the oven. Maybe a couple of other things rarely.
Normally stovetop, used like a hot flat top at a restaurant. I would destroy a typical fancy non-stick skillet in days the way I like to sear and toast things. I have in fact. :)

This id all very helpful - I usually use hot water and a paper towel, and I leave it to dry over the stove. I’ll start to just wipe it dry and then put away into its drawer (we don’t have space for hanging pots/pans).

I have similar challenges keeping a ridged pan both clean and seasoned. I understand the idea that you should avoid aggressively cleaning it, but I find that difficult after cooking fish or marinated meats, unless you want to taste the last meal in your next dish....!