Prepare your onions by mincing them finely with a knife or use a food processor as a shortcut. The pieces should be smaller than your pinky finger nail.
In a medium saucepan over medium-high heat, melt the butter with the olive oil.
Once the butter is melted and the olive oil is shimmering, add the minced onion and stir well to coat.
Cook the onion for 10 minutes, stirring very frequently to prevent burning with a silicone spatula or wooden spoon.
After 10 minutes, reduce the heat to low and add a pinch of salt. Stir well.
Cook the onions for an additional 35-45 minutes, stirring often, until they are a deep golden color and have a sweet taste. This is a recipe that takes a lot of time and attention, although it is very simple to do. I suggest preparing this while doing dishes or working in the kitchen, as you sort of have to nurse the onions to ensure they do not burn. Just give them a nice stir each time you walk by the stove.
Once the onions are cooked through, cool slightly in the pan, then transfer to a small jar (a half pint size should do). Once the onions are completely cool, add a lid to the jar and store in the fridge for up to one week.