In the bowl of your stand mixer, put the flour, salt, sugar, and yeast. Measure the eggs, milk and butter.
Pour the milk and egg in the bowl and start mixing with the hook for 4 minutes on first speed.Keep mixing for 10 more minutes on second speed.Don't forget to scrape the bowl and the hook from time to time.Add the soft butter and mix for 5 minutes on second speed until well combined.Form the dough into a ball, cover and allow to proof for an hour at room temperature.
Fold the brioche and shape it as a ball. Cover with saran wrap and place in the freezer for 30 minutes.
Divide the dough in 6 pieces (2.8 oz - 80 g).
Pre-shape the sliders and let rest for 10 minutes, covered with a kitchen cloth or a plastic.Shape the slider buns and put them on a baking sheet with parchment paper.Cover with a kitchen cloth and proof for 1:30.
Preheat the oven at 320°F - 160°C.When the oven is ready, egg wash the buns with the beaten egg and sprinkle with sesame seeds.
Bake for about 20 minutes and allow to cool down on a cooling rack.
When shaping the buns, don't use flour if they stick to the surface, spray lightly with oil.