In a small saucepan on low heat, melt the butter. It will begin to bubble and look very frothy, then slowly it will look clear and begin to darken. When it starts to smell nutty, keep a close watch on it, stirring frequently. Turn off the heat as soon as you see a few brown bits at the bottom of the pan. Set aside to cool.
Preheat the oven to 180 C and generously grease 6 muffin moulds with butter.
In a mixing bowl, combine the almond flour, all-purpose flour, sugar and salt. Mix well.
Add the egg whites and vanilla and whisk well, but do not over-mix. The mixture will smoothen out at the end.
Now add the browned butter (I like to add the browned bits at the bottom too, you can leave them out if you prefer), and stir gently but thoroughly till the butter is well-combined with the rest of the mixture and you have a smooth batter.
Divide the batter equally among the moulds, filling each only halfway. Bake for 13 to 15 minutes, until the cakes have puffed a little and are golden-brown on the top. I needed to bake them for a few extra minutes, depending on your oven, you may need to as well.
Set aside to cool, then using a small blunt knife, gently remove them from the moulds. They tend to stick, so don't let them sit in the pan too long after they've cooled. Store at room temperature for 2 to 3 days in an airtight tin, then refrigerate or freeze. Enjoy warm with tea or coffee!