The most time consuming part of this is grilling the onions, so let's start that before anything else. Add the vegan butter and oil to a pan over medium / medium high heat. Once melted and bubbling, add your onions and stir to coat. Stir it frequently, and after 10 minutes, add in a pinch of salt and sugar, which will help with the flavor and browning.
You can try to multitask and grill the onions while you prepare the rest of the burger components, but either way, just keep an eye on them and make sure they don't brown too fast, or even worse, burn! Lower the heat as needed, stir frequently, and deglaze with some water if they stick to the pan. They should be perfect in about 45 minutes to 1 hour.
Optionally, you can add 1 Tbsp of balsamic vinegar and 1/4 - 1/2 cup of vegan beef broth. Then just cook them down and reduce the broth. This will add some extra beefy flavor! Once they are done, remove from the heat and reserve.