Place the butter in a non-stick pan and heat until it melts and turns a golden brown and smells like roasted nuts. Remove from the heat and let it cool.
Crack the two eggs into a clean bowl. Add the brown sugar and whisk until the eggs-sugar mix is pale, frothy and thick.
Add the salt, lemon rind, lemon juice, vanilla and fold through to mix.
Add the sifted flour and fold through until just combined.
Add the cooled brown butter and fold through until the butter has mixed well with the batter.
Cover the bowl and refrigerate for at least 4 hours (or overnight or up to 2 days).
Prepare the madeleine pans (prepare 2 madeleine pans for 1 batch as this makes about 16 madeleines). Melt some butter, and using a pastry brush, brush each cavity thoroughly with a thin layer of melted butter. Keep the tray in the freezer until the butter has hardened. Apply another coat of thin butter and dust the cavities with some flour.
Keep the prepared tray in the fridge or freezer to completely set (keep it in the fridge if it's for more than 1 hour).
Preheat oven to 375°F / 190°C. Fill each cavity about ¾ of the way with cake batter - about 1 heaped tbsp.
Bake in the oven for 12 - 15 minutes, until the edges are a golden brown and the center is puffed up. (the precise time will vary based on your oven temperature).
Remove from the oven and let it cool for a few minutes. While the cakes are still warm, pop them out of the pan (they should come out easily, but use a spoon to loosen them up gently if needed).
Eat while still warm or at room temperature with a dusting of sugar OR with the passion fruit glaze.
Passion Fruit Glaze
While the brown butter madeleines are baking, whisk the confectioner's sugar and passion fruit pulp together until you have a thick, pourable glaze. Add more passion fruit as required to thin out the glaze, or more confectioner's sugar to thicken the glaze.
Dip half of each madeleine in the glaze to coat, and place them on a parchment paper or cooling tray.
Eat while warm, or let the glaze set and serve at room temperature.