In a stand-up mixer with a dough hook attachment, mix salt, flour, and sugar.
Dilute the yeast in the water, add it to the first mix, add the eggs and mix gently on low speed for 10 minutes. The dough should be elastic and shiny.
Add the room temperature butter, cut into small dice, mix well until the butter is completely incorporated into the dough, add the lemon zest, mix for another minute. Allow it to rest in the mixer bowl covered with a dish towel for one hour.
Flatten the dough to remove some of the gas and make a nice ball. Let rest in the fridge for 30 minutes.
Roll out the dough and place it into a round baking ring of 20cm (8 inches) diameter on a baking pan with parchment paper. Let rise for 60 minutes. If you don’t have a baking ring, you can use a round baking dish lined with parchment paper.
Turn your oven at 180ºc (375ºF), brush the top of the brioche with the egg yolk, add the sugar and bake for around 20 minutes.
Melt butter and sugar on the stove and spread it on top of the brioche, and cook 10 more minutes
Let rest on a cooling rack.