Start by melting the butter in the microwave and then set aside to cool to room temperature.
Butter the madeleine tray with some softened lightly-salted butter.
In a large bowl, whisk the 2 eggs and the 2 egg yolks together, along with the sugar for 1 minute.
Add the honey, the vegetable oil and the lemon zest, and whisk for 1 minute.
Add the flour and baking powder and whisk just until you can't see the flour any more.
Check that the butter is at room temperature by dipping your finger in it. It shouldn't feel hot to the touch. Alternatively, you can check with a thermoter that it's around 35 degrees (but honestly I always just check with my finger).
Pour the melted butter into the batter and mix until fully incorporated.
Fill the buttered madeleine tray with batter, up to 3/4 of the way for each mold.
Place the tray in the fridge and let the dough sit for at least 20 minutes.
Preheat your oven to 210 C.
Place the tray in the oven and let the madeleines bake for 6 minutes. Then turn down the temperature of the oven to 180 C, and keep the door open for about 10/15 seconds so that the internal temperature can come down quickly.
Bake for another 4 minutes, or until the madeleines are golden brown on the edges and a toothpick inserted into the center comes out clean.
Immediately remove the madeleines onto a cutting board to cool for a few minutes, then transfer them to a cooling rack.