Cooking and heating water with electricity off-grid is usually impractical but there are exceptions. In some cases the relatively large power loads can be used without affecting house battery¹⁾ state of charge:

• while driving²⁾ the alternator makes a great deal of excess power. Class C RV owners often run a crock-pot while driving from site to site.
• if a generator is being run to charge batteries cooking loads can be added
• with lead-chemistry batteries, later in the day excess solar power is available. The actual amount of excess power will depend on what your panels+controller can put out
• with lithium batteries, power can be consumed at any time since Li doesn't need to reach full charge.

In general DC power³⁾ is used for warming or very slow cooking. Part of this is due to the limits of cigarette lighter outputs, typically 120w (10A x 12v). The “catch-22” is that most people don't drive their vehicle sufficient hours to do real cooking off DC.

Higher power is common with AC devices but one must have the power to run it, and to recharge the battery bank afterwards.

• immersion (loop) heaters for DC are typically 150w. Example: RoadPro beverage heater (138w). Caveats:
  • heat only water with them; anything else baked on is extremely difficult to clean off the coils
  • carry extra fuses in case you blow the ciggy port fuse. Know where the fuses go.
  • unplug before removal from water to avoid overheating the element
  • have a safe place planned to set them down before heating; they will be very hot and can melt/burn surfaces after removal from the water
• heated lunchboxes/warmers are large enough to hold hot lunches. They are typically better suited to warming precooked meals rather than cooking from scratch. They come in “lunchbox” and “suitcase” styles.
  • lunchbox - hard exterior, typically better insulated tops and higher power.
    • RoadPro RPSC-197 (12v/120w) - the most popular model
    • Travelisimo 1.5L warmer (12v/40w)
    • there are several externally-ribbed RoadPro clones but they have less documentation: Zento, Vaygway, ZonePro. Of these, only the ZonePro lists wattage (120w).
  • suitcase - soft exterior, often lightly-insulated tops and lower heating power.
    • Hot Logic Mini - a popular model. (12v/45w)
    • Sabotheat (12v/90w). Note: has heat levels and timer.
• crockpot/slow cooker typically require many hours of cooking.
  • RoadPro 1wt slow cooker (96w), which has a lid retainer for mobile use. Specs say it heats from 140F - 170F.
• heated mugs can be used to keep beverages hot, or heat small amounts of water for tea, coffee. Warm canned soup, etc. Example: Wagan heated mug (12v/24w).
• mini rice cookers. Example: mini rice cooker (12v/100w). Recommended by dannydevitosmgnmdong. See also /r/urbancarlivingcooking.

Analog cooking appliances (knobs, not electronics) run fine off inexpensive MSW inverters.

• crock pots typically take 125w-200w on HI and half that value on LO.
• Instant Pots run 700w to 1200w, depending on size
• mini rice cookers. Normal rice cookers run ~300w but some of the smaller travel ones use less. Example: Dash 200w 1L travel rice cooker (200w).
• immersion (loop) heaters for AC are typically 300w although NOS⁴⁾ versions can be found for 200w. Example: Norpro 559 immersion heater. (300w)
• this two-burner hotplate has a 600w coil on one side that may be usable in a van.
• small 120vac lunchboxes, as for bento. Example: FIKNEE lunchbox heater, rated 200w and used by Psyckosama.

There are some major ways the two differ:

• cost - used crockpots are cheap in thrift stores
• current - crockpots demand much less current, which may also increase the cost of wiring, batteries, and inverter, but…
• energy use - instant pots will generally use far fewer watt-hours to took the same meal⁵⁾

also see this post

see this article

Power/time saving

• Preheating water on the dash or elsewhere
• heating only the required amount of water
• reducing power level after reaching a boils (ie, reduce power to simmer)
• covering pots while heating
• pre-soaking beans (overnight) rice (up to an hour), etc

Cleaning

• use parchment paper, foil to line crocks
• lightly oil crocks before cooking to reduce sticking
• immersion heaters might best be used for heating plain water, as the loops can be difficult to clean

• water heating power calculator