tl;dr: Possible? Yes. Practical? No.
Some quick back of the envelope math... First of all, your stated 0.72kWh average, on a stove with a 1200W (1.2kW) power draw, means you're only getting 36 minutes of runtime before you need to recharge (0.72kWh/1.2kW = 0.6h). But sometimes you may want to cook something that takes a little longer, so let's be more generous and plan for 1 hour of cooking, or 1.2kW of storage.
Suppose you use lithium-ion batteries. A common lithium ion cell has a nominal voltage of 3.6V, and usually somewhere around 3000mAh of storage, for approximately $5. That works out to approximately 10-12W of energy storage per cell. Here's one example: https://www.18650batterystore.com/Panasonic-18650-p/panasonic-ncr18650b.htm .
If we were to construct a battery using these cells, we would need over 100 of them, which would be fairly bulky, and already we have $500 in cost not including the connections and electronics to make it all work.
If instead we used a cheaper battery chemistry, such as lead acid, it would greatly increase the size and weight, and it would be a stretch to call such a device "portable". Here is a single-battery solution that would provide the needed 1200W, but it costs $290 and weighs 65lbs (30kg): https://www.batteriesplus.com/battery/sla-sealed-lead-acid/12/wkdc12=100p
And $300-500 could buy quite a lot of kerosene or propane for a more conventional portable stove, which would provide much more than an hour of runtime.