Hi Nathan and welcome to BPL.
I have the same mug as part of the Lite Trail Solid Fuel Cook System: http://litetrail.com/shop/litetrail-titanium-solid-fuel-cook-system.
If I'm hiking with one of my kids, I'll heat up four cups of water per day using one .5oz Esbit tablet with this system. Two cups will be used for a freezer bag dinner that we'll share and the other two cups will be for hot chocolate or coffee.
The key for me with a 550ml mug is cooking in a freezer bag. I heat up the water until it starts to sing and not a full rolling boil. This is more than sufficient to warm/rehydrate the food for me and only takes 1/2 of the tablet to accomplish. If I'm with one of my kids, they'll have their own mug and I'll serve their portion into that. If we are dry camping, I'll bring an extra freezer bag to line their mug with so we won't have to waste water cleaning their pot. As soon as the water is hot enough (judgment call / starts making noise), I'll blow the fire out, pour the water into the freezer bag meal, and put that into my cozy for ~ 10 minutes. I'll eat my portion out of the bag.
After dinner I'll heat up another two cups of water, let the tablet burn completely out, and again, split it with my kid and enjoy some hot chocolate or save it for next morning's coffee.
